We present a novel nonperturbative approach for calculating the form factors of the quark-gluon v... more We present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex, in a general covariant gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quarkgluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in the Landau gauge, in order to make contact with the results of lattice simulations performed in this particular gauge. The most demanding technical aspect involves the calculation of certain (fully-dressed) auxiliary three-point functions, using lattice data as input for the gluon propagators appearing in their diagrammatic expansion. The numerical evaluation of the relevant form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum) is carried out in detail, finding rather good agreement with the available lattice data. Most notably, a concrete mechanism is proposed for explaining the puzzling divergence of one of these form factors observed in lattice simulations.
We consider a minimal nonlinearly realized electroweak theory where mass generation happens à la ... more We consider a minimal nonlinearly realized electroweak theory where mass generation happens à la Stückelberg. Deformation of the nonlinearly realized gauge symmetry is controlled by functional methods. The Weak Power Counting allows to select uniquely the Hopf algebra of the theory and gives definite predictions on the Beyond-the-Standard Model (BSM) sector of the theory: the latter includes one CP-odd and two charged physical scalars (in addition to the Higgs-like CP-even resonance). The model interpolates between a purely Stückelberg and a Higgs scenario. It can be used in order to check whether the presence of a Stückelberg mass component can already be excluded on the basis of the existing LHC7-8 data.
CLEO/Europe. 2005 Conference on Lasers and Electro-Optics Europe, 2005., 2005
The aim of this contribution is two-fold. We propose a new approach to the search for vortex solu... more The aim of this contribution is two-fold. We propose a new approach to the search for vortex solutions of a general nonlinear equation that describes not only both optical and Bose-Einstein condensates discrete-symmetry systems but also more general situations. A general expression for symmetric vortex solutions will be proved by showing that they are angular Bloch modes associated to the
The generalization of the pinch technique to all orders in perturbation theory is presented. The ... more The generalization of the pinch technique to all orders in perturbation theory is presented. The effective Green's functions constructed with this procedure are singled out in a unique way through the full exploitation of the underlying Becchi-Rouet-Stora-Tyutin symmetry. A simple all-order correspondence between the pinch technique and the background field method in the Feynman gauge is established.
We study a fundamental, all order cancellation operating between graphs of distinct kinematic nat... more We study a fundamental, all order cancellation operating between graphs of distinct kinematic nature, which allows for the construction of gauge-independent effective self-energies, vertices, and boxes at arbitrary order.
We present a new truncation scheme for the Schwinger-Dyson equations of QCD that respects gauge i... more We present a new truncation scheme for the Schwinger-Dyson equations of QCD that respects gauge invariance at any level of the dressed loop expansion. When applied to the gluon selfenergy, it allows for its non-perturbative treatment without compromising the transversality of the solution, even when entire sets of diagrams (most notably the ghost loops) are omitted, or treated perturbatively.
We review the most recent results, derived within the combined framework of the pinch technique a... more We review the most recent results, derived within the combined framework of the pinch technique and the background field method, describing certain QCD nonperturbative properties.
In this article we study in detail the prospects of determining the infrared finite QCD effective... more In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.
We show that the (gauge fixed) classical action of the Color Glass Condensate is invariant under ... more We show that the (gauge fixed) classical action of the Color Glass Condensate is invariant under a suitable Becchi-Rouet-Stora-Tyutin symmetry, that holds after the gluon modes are split into their fast, semi-fast and soft components, according to the longitudinal momenta they carry. This entails the existence of a corresponding Slavnov-Taylor identity which in turn strongly constrains the effective field theory arising when integrating out the semi-fast modes. Specifically, we prove that this identity guarantees the gauge invariance of the resulting effective theory. In addition, we use it to demonstrate that the integration over the semi-fast modes does not deform the classical Yang-Mills equations of motion, thus validating a key assumption in the usual procedure adopted when deriving the renormalization group equation governing the evolution with energy of the effective theory. As far as the latter are concerned, we finally prove that its functional form is common, and it is determined by symmetries arguments alone. The formal properties of these equations valid in different regimes and/or approximations (e.g., the JIMWLK equation and its BFKL limit) can be therefore derived in a unified setting within this algebraic approach.
We study the non-perturbative behavior of two versions of the QCD effective charge, one obtained ... more We study the non-perturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various of the ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the non-perturbative dynamics of the quantities composing the two effective charges.
We introduce a physical scalar sector in a SU(2)⊗U(1) electroweak theory in which the gauge group... more We introduce a physical scalar sector in a SU(2)⊗U(1) electroweak theory in which the gauge group is realized non linearly. By invoking theoretical as well as experimental constraints, we build a phenomenologically viable model in which a minimum of four scalar resonances appear, and the mass of the CP even scalar is controlled by a vacuum expectation value; however, the masses of all other particles (both matter as well as vector boson fields) are unrelated to spontaneous symmetry breaking and generated by the Stückelberg mechanism. We evaluate in this model the CP-even scalar decay rate to two photons and use this amplitude to perform a preliminary comparison with the recent LHC measurements. As a result, we find that the model exhibits a preference for a negative Yukawa coupling between the top quark and the CP-even resonance.
We study the structure and non-perturbative properties of a special Green's function, u(q 2 ), wh... more We study the structure and non-perturbative properties of a special Green's function, u(q 2 ), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. It turns out that, in the Landau gauge, u(q 2 ) can be determined from a dynamical equation, whose main ingredients are the gluon propagator and the ghost dressing function, integrated over all physical momenta. Using as input for these two (infrared finite) quantities recent lattice data, we obtain an indirect determination of u(q 2 ). The results of this mixed procedure are in excellent agreement with those found previously on the lattice, through a direct simulation of this function. Most importantly, in the deep infrared the function deviates considerably from the value associated with the realization of the aforementioned confinement scenario. In addition, the dependence of u(q 2 ), and especially of its value at the origin, on the renormalization point is clearly established. Some of the possible implications of these results are briefly discussed.
We show that the application of the pinch technique to the conventional Schwinger-Dyson equations... more We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the standard case, the new equation for the gluon self-energy can be truncated gauge invariantly at any order in the dressed loop expansion. The construction is streamlined by resorting to the Batalin-Vilkovisky formalism which allows for a concise treatment of all the quantities appearing in the intermediate steps. The theoretical and phenomenological implications of this novel non-perturbative framework are discussed in detail.
We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function... more We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green's functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their definition, is the freezing at a common finite (non-vanishing) value, in agreement with a plethora of theoretical and phenomenological expectations. We discuss the sizable discrepancy between the freezing values obtained from the present lattice analysis and the corresponding estimates derived from several phenomenological studies, and attribute its origin to the difference in the gauges employed. A particular toy calculation suggests that the modifications induced to the non-perturbative gluon propagator by the gauge choice may indeed account for the observed deviation of the freezing values.
We show that the application of a novel gauge invariant truncation scheme to the Schwinger-Dyson ... more We show that the application of a novel gauge invariant truncation scheme to the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared finite gluon propagator and a divergent ghost propagator, in qualitative agreement with recent lattice data.
ABSTRACT We study in detail the impact of dynamical quarks on the gluon mass generation mechanism... more ABSTRACT We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major improvement compared to the analysis presented in Phys. Rev. D86 (2012) 014032, where the behaviour of the gluon propagator in the deep infrared was estimated through numerical extrapolation. The resulting nonlinear system is then treated numerically, yielding unique solutions for the modified gluon mass and the quenched gluon propagator, which fully confirm the picture put forth recently in several continuum and lattice studies. In particular, an infrared finite gluon propagator emerges, whose saturation point is considerably suppressed, due to a corresponding increase in the value of the gluon mass. This characteristic feature becomes more pronounced as the number of active quark families increases, and can be deduced from the infrared structure of the kernel entering in the gluon mass equation.
We devise an algebraic procedure for the evaluation of Green's functions in SU (N ) Yang-Mills th... more We devise an algebraic procedure for the evaluation of Green's functions in SU (N ) Yang-Mills theory in the presence of a non-trivial background field. In the ghost-free sector the dependence of the vertex functional on the background is shown to be uniquely determined by the Slavnov-Taylor identities in terms of a certain 1-PI correlator of the covariant derivatives of the ghost and the anti-ghost fields. At non-vanishing background this amplitude is shown to encode the quantum deformations to the tree-level background-quantum splitting. The approach only relies on the functional identities of the model (Slavnov-Taylor identities, b-equation, anti-ghost equation) and thus it is valid beyond perturbation theory, and in particular in a lattice implementation of the background field method. As an example of the formalism we analyze the ghost two-point function and the Kugo-Ojima function in an instanton background in SU (2) Yang-Mills theory, quantized in the background Landau gauge.
We construct explicitly the canonical transformation that controls the full dependence (local and... more We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is nothing but a direct field-theoretic generalization of the Lie transform of classical analytical mechanics, we comment on a number of possible applications, and in particular the non perturbative implementation of the background field method on the lattice, the background field formulation of the two particle irreducible formalism, and, finally, the formulation of the Schwinger-Dyson series in the presence of topologically non-trivial configurations.
We present a novel nonperturbative approach for calculating the form factors of the quark-gluon v... more We present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex, in a general covariant gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quarkgluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in the Landau gauge, in order to make contact with the results of lattice simulations performed in this particular gauge. The most demanding technical aspect involves the calculation of certain (fully-dressed) auxiliary three-point functions, using lattice data as input for the gluon propagators appearing in their diagrammatic expansion. The numerical evaluation of the relevant form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum) is carried out in detail, finding rather good agreement with the available lattice data. Most notably, a concrete mechanism is proposed for explaining the puzzling divergence of one of these form factors observed in lattice simulations.
We consider a minimal nonlinearly realized electroweak theory where mass generation happens à la ... more We consider a minimal nonlinearly realized electroweak theory where mass generation happens à la Stückelberg. Deformation of the nonlinearly realized gauge symmetry is controlled by functional methods. The Weak Power Counting allows to select uniquely the Hopf algebra of the theory and gives definite predictions on the Beyond-the-Standard Model (BSM) sector of the theory: the latter includes one CP-odd and two charged physical scalars (in addition to the Higgs-like CP-even resonance). The model interpolates between a purely Stückelberg and a Higgs scenario. It can be used in order to check whether the presence of a Stückelberg mass component can already be excluded on the basis of the existing LHC7-8 data.
CLEO/Europe. 2005 Conference on Lasers and Electro-Optics Europe, 2005., 2005
The aim of this contribution is two-fold. We propose a new approach to the search for vortex solu... more The aim of this contribution is two-fold. We propose a new approach to the search for vortex solutions of a general nonlinear equation that describes not only both optical and Bose-Einstein condensates discrete-symmetry systems but also more general situations. A general expression for symmetric vortex solutions will be proved by showing that they are angular Bloch modes associated to the
The generalization of the pinch technique to all orders in perturbation theory is presented. The ... more The generalization of the pinch technique to all orders in perturbation theory is presented. The effective Green's functions constructed with this procedure are singled out in a unique way through the full exploitation of the underlying Becchi-Rouet-Stora-Tyutin symmetry. A simple all-order correspondence between the pinch technique and the background field method in the Feynman gauge is established.
We study a fundamental, all order cancellation operating between graphs of distinct kinematic nat... more We study a fundamental, all order cancellation operating between graphs of distinct kinematic nature, which allows for the construction of gauge-independent effective self-energies, vertices, and boxes at arbitrary order.
We present a new truncation scheme for the Schwinger-Dyson equations of QCD that respects gauge i... more We present a new truncation scheme for the Schwinger-Dyson equations of QCD that respects gauge invariance at any level of the dressed loop expansion. When applied to the gluon selfenergy, it allows for its non-perturbative treatment without compromising the transversality of the solution, even when entire sets of diagrams (most notably the ghost loops) are omitted, or treated perturbatively.
We review the most recent results, derived within the combined framework of the pinch technique a... more We review the most recent results, derived within the combined framework of the pinch technique and the background field method, describing certain QCD nonperturbative properties.
In this article we study in detail the prospects of determining the infrared finite QCD effective... more In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.
We show that the (gauge fixed) classical action of the Color Glass Condensate is invariant under ... more We show that the (gauge fixed) classical action of the Color Glass Condensate is invariant under a suitable Becchi-Rouet-Stora-Tyutin symmetry, that holds after the gluon modes are split into their fast, semi-fast and soft components, according to the longitudinal momenta they carry. This entails the existence of a corresponding Slavnov-Taylor identity which in turn strongly constrains the effective field theory arising when integrating out the semi-fast modes. Specifically, we prove that this identity guarantees the gauge invariance of the resulting effective theory. In addition, we use it to demonstrate that the integration over the semi-fast modes does not deform the classical Yang-Mills equations of motion, thus validating a key assumption in the usual procedure adopted when deriving the renormalization group equation governing the evolution with energy of the effective theory. As far as the latter are concerned, we finally prove that its functional form is common, and it is determined by symmetries arguments alone. The formal properties of these equations valid in different regimes and/or approximations (e.g., the JIMWLK equation and its BFKL limit) can be therefore derived in a unified setting within this algebraic approach.
We study the non-perturbative behavior of two versions of the QCD effective charge, one obtained ... more We study the non-perturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various of the ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the non-perturbative dynamics of the quantities composing the two effective charges.
We introduce a physical scalar sector in a SU(2)⊗U(1) electroweak theory in which the gauge group... more We introduce a physical scalar sector in a SU(2)⊗U(1) electroweak theory in which the gauge group is realized non linearly. By invoking theoretical as well as experimental constraints, we build a phenomenologically viable model in which a minimum of four scalar resonances appear, and the mass of the CP even scalar is controlled by a vacuum expectation value; however, the masses of all other particles (both matter as well as vector boson fields) are unrelated to spontaneous symmetry breaking and generated by the Stückelberg mechanism. We evaluate in this model the CP-even scalar decay rate to two photons and use this amplitude to perform a preliminary comparison with the recent LHC measurements. As a result, we find that the model exhibits a preference for a negative Yukawa coupling between the top quark and the CP-even resonance.
We study the structure and non-perturbative properties of a special Green's function, u(q 2 ), wh... more We study the structure and non-perturbative properties of a special Green's function, u(q 2 ), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. It turns out that, in the Landau gauge, u(q 2 ) can be determined from a dynamical equation, whose main ingredients are the gluon propagator and the ghost dressing function, integrated over all physical momenta. Using as input for these two (infrared finite) quantities recent lattice data, we obtain an indirect determination of u(q 2 ). The results of this mixed procedure are in excellent agreement with those found previously on the lattice, through a direct simulation of this function. Most importantly, in the deep infrared the function deviates considerably from the value associated with the realization of the aforementioned confinement scenario. In addition, the dependence of u(q 2 ), and especially of its value at the origin, on the renormalization point is clearly established. Some of the possible implications of these results are briefly discussed.
We show that the application of the pinch technique to the conventional Schwinger-Dyson equations... more We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the standard case, the new equation for the gluon self-energy can be truncated gauge invariantly at any order in the dressed loop expansion. The construction is streamlined by resorting to the Batalin-Vilkovisky formalism which allows for a concise treatment of all the quantities appearing in the intermediate steps. The theoretical and phenomenological implications of this novel non-perturbative framework are discussed in detail.
We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function... more We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green's functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their definition, is the freezing at a common finite (non-vanishing) value, in agreement with a plethora of theoretical and phenomenological expectations. We discuss the sizable discrepancy between the freezing values obtained from the present lattice analysis and the corresponding estimates derived from several phenomenological studies, and attribute its origin to the difference in the gauges employed. A particular toy calculation suggests that the modifications induced to the non-perturbative gluon propagator by the gauge choice may indeed account for the observed deviation of the freezing values.
We show that the application of a novel gauge invariant truncation scheme to the Schwinger-Dyson ... more We show that the application of a novel gauge invariant truncation scheme to the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared finite gluon propagator and a divergent ghost propagator, in qualitative agreement with recent lattice data.
ABSTRACT We study in detail the impact of dynamical quarks on the gluon mass generation mechanism... more ABSTRACT We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major improvement compared to the analysis presented in Phys. Rev. D86 (2012) 014032, where the behaviour of the gluon propagator in the deep infrared was estimated through numerical extrapolation. The resulting nonlinear system is then treated numerically, yielding unique solutions for the modified gluon mass and the quenched gluon propagator, which fully confirm the picture put forth recently in several continuum and lattice studies. In particular, an infrared finite gluon propagator emerges, whose saturation point is considerably suppressed, due to a corresponding increase in the value of the gluon mass. This characteristic feature becomes more pronounced as the number of active quark families increases, and can be deduced from the infrared structure of the kernel entering in the gluon mass equation.
We devise an algebraic procedure for the evaluation of Green's functions in SU (N ) Yang-Mills th... more We devise an algebraic procedure for the evaluation of Green's functions in SU (N ) Yang-Mills theory in the presence of a non-trivial background field. In the ghost-free sector the dependence of the vertex functional on the background is shown to be uniquely determined by the Slavnov-Taylor identities in terms of a certain 1-PI correlator of the covariant derivatives of the ghost and the anti-ghost fields. At non-vanishing background this amplitude is shown to encode the quantum deformations to the tree-level background-quantum splitting. The approach only relies on the functional identities of the model (Slavnov-Taylor identities, b-equation, anti-ghost equation) and thus it is valid beyond perturbation theory, and in particular in a lattice implementation of the background field method. As an example of the formalism we analyze the ghost two-point function and the Kugo-Ojima function in an instanton background in SU (2) Yang-Mills theory, quantized in the background Landau gauge.
We construct explicitly the canonical transformation that controls the full dependence (local and... more We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is nothing but a direct field-theoretic generalization of the Lie transform of classical analytical mechanics, we comment on a number of possible applications, and in particular the non perturbative implementation of the background field method on the lattice, the background field formulation of the two particle irreducible formalism, and, finally, the formulation of the Schwinger-Dyson series in the presence of topologically non-trivial configurations.
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Papers by D. Binosi