Research Interests:
Research Interests:
En aquest treball estudiem la Dinàmica de sistemes relativistes de dues partícules puntuals en acció directa, és a dir, sense camps retardats que propaguin la interacció. En una primera part desenvolupem el marc general adient per a... more
En aquest treball estudiem la Dinàmica de sistemes relativistes de dues partícules puntuals en acció directa, és a dir, sense camps retardats que propaguin la interacció. En una primera part desenvolupem el marc general adient per a aquest tipus de plantejament (Teoria dels sistemes amb lligams), i fem a continuació una anàlisi detallada del model Lagrangià singular de-DGL. Després estudiem
Research Interests: Philosophy and Humanities
The analysis of the equivalence between the Hamiltonian and Lagrangian formalisms, for a sp(2) BRST theory, is achieved. The proof of this equivalence, apart from its intrinsic importance, allows the explanation of some results which seem... more
The analysis of the equivalence between the Hamiltonian and Lagrangian formalisms, for a sp(2) BRST theory, is achieved. The proof of this equivalence, apart from its intrinsic importance, allows the explanation of some results which seem artificially implanted in the theory: the structure of the extended spaces, and the form of the master equation. As a new image on the BRST operator, this paper suggests that its action can be split into a canonical part and a noncanonical part.
Research Interests:
We exhibit a new method of constructing non-Lorentzian models by applying a method we refer to as starting from a so-called seed Lagrangian. This method typically produces additional constraints in the system that can drastically alter... more
We exhibit a new method of constructing non-Lorentzian models by applying a method we refer to as starting from a so-called seed Lagrangian. This method typically produces additional constraints in the system that can drastically alter the physical content of the model. We demonstrate our method for particles, scalars and vector fields.
Research Interests:
Research Interests:
We construct the electric and magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity theories using the isomorphism of Newton-Hooke± and (A-)dS Carroll algebras in (1+1)-spacetime dimensions. The starting point is the... more
We construct the electric and magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity theories using the isomorphism of Newton-Hooke± and (A-)dS Carroll algebras in (1+1)-spacetime dimensions. The starting point is the non-relativistic and Carroll version of Jackiw-Teitelboim gravity without restrictions on the geometry studied in [1].
Research Interests:
The BRST cohomology on local functionals is analysed at all ghost numbers for effective bosonic D-strings and generalizations thereof, in target spaces of any dimension and geometry, and for any number of abelian world-sheet gauge fields.... more
The BRST cohomology on local functionals is analysed at all ghost numbers for effective bosonic D-strings and generalizations thereof, in target spaces of any dimension and geometry, and for any number of abelian world-sheet gauge fields. The classification of the corresponding action functionals is part of the results and reveals, among others, Born-Infeld type actions. Furthermore the analysis covers the classification of all rigid symmetries, dynamical conservation laws, first order consistent deformations, and candidate gauge anomalies of the models under study. Among the deformations, there are nonabelian Born-Infeld models in a sigma model formulation. PACS numbers: 02.90.+p, 11.10.Kk, 11.25.-w, 11.30.-j
Research Interests:
We study a class of extensions of the [Formula: see text]-contracted Poincaré algebra under the hypothesis of generalizing the Bargmann algebra and its central charge. As we will see this type of contractions will lead in a natural way to... more
We study a class of extensions of the [Formula: see text]-contracted Poincaré algebra under the hypothesis of generalizing the Bargmann algebra and its central charge. As we will see this type of contractions will lead in a natural way to consider the codajoint Poincaré algebra and some of their contractions. Among them there is one such that considering the quotient of it by a suitable ideal, the (stringy) [Formula: see text]-brane Galilei algebra is recovered.
Research Interests:
We construct free Lie algebras which, together with the algebra of spatial rotations, form infinite-dimensional extensions of finite-dimensional Galilei Maxwell algebras appearing as global spacetime symmetries of extended... more
We construct free Lie algebras which, together with the algebra of spatial rotations, form infinite-dimensional extensions of finite-dimensional Galilei Maxwell algebras appearing as global spacetime symmetries of extended non-relativistic objects and non-relativistic gravity theories. We show how various extensions of the ordinary Galilei algebra can be obtained by truncations and contractions, in some cases via an affine Kac-Moody algebra. The infinite-dimensional Lie algebras could be useful in the construction of generalized Newton-Cartan theories gravity theories and the objects that couple to them.
Research Interests:
We study systematically various extensions of the Poincaré superalgebra. The most general structure starting from a set of spinorial superchargesQαis a free Lie superalgebra that we discuss in detail. We explain how this universal... more
We study systematically various extensions of the Poincaré superalgebra. The most general structure starting from a set of spinorial superchargesQαis a free Lie superalgebra that we discuss in detail. We explain how this universal extension of the Poincaré superalgebra gives rise to many other algebras as quotients, some of which have appeared previously in various places in the literature. In particular, we show how some quotients can be very neatly related to Borcherds superalgebras. The ideas put forward also offer some new angles on exotic branes and extended symmetry structures in M-theory.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
ABSTRACT Key words Space-time symmetries, non-linear realization, super p-branes PACS 11.25.-w,11.10.Ef We will show how the theory of non-linear realizations can be used to naturally incorporate kappa transfor-mations for the superpoint... more
ABSTRACT Key words Space-time symmetries, non-linear realization, super p-branes PACS 11.25.-w,11.10.Ef We will show how the theory of non-linear realizations can be used to naturally incorporate kappa transfor-mations for the superpoint particle. Similar results also hold for a general super p-brane, however we must in these cases include an additional Lorentz transformation.
Research Interests:
Research Interests:
We construct two possible candidates for the non-relativistic bms_4 algebra in 4 space-time dimensions by contracting the original relativistic bms_4 algebra. The bms_4 algebra is infinite-dimensional, and it contains the generators of... more
We construct two possible candidates for the non-relativistic bms_4 algebra in 4 space-time dimensions by contracting the original relativistic bms_4 algebra. The bms_4 algebra is infinite-dimensional, and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms_4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realisation of one these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realisation of the relativistic bms_4 algebra using a free Klein-Gordon field.
Research Interests:
Research Interests:
We study the space-time symmetries of the actions obtained by expanding the action for a massive free relativistic particle around the Galilean action. We obtain all the point space-time symmetries of the post-Galilean actions by working... more
We study the space-time symmetries of the actions obtained by expanding the action for a massive free relativistic particle around the Galilean action. We obtain all the point space-time symmetries of the post-Galilean actions by working in canonical space. We also construct an infinite collection of generalized Schrodinger algebras parameterized by an integer $M$, with $M=0$ corresponding to the standard Schrodinger algebra. We discuss the Schrodinger equations associated to these algebras, their solutions and projective phases.
Research Interests:
We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study... more
We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.
Research Interests:
We construct the non-relativistic and Carrollian versions of Jackiw-Teitelboim gravity. In the second order formulation, there are no divergences in the non-relativistic and Carrollian limits. Instead, in the first order formalism, some... more
We construct the non-relativistic and Carrollian versions of Jackiw-Teitelboim gravity. In the second order formulation, there are no divergences in the non-relativistic and Carrollian limits. Instead, in the first order formalism, some divergences can be avoided by starting from a relativistic BF theory with (A)dS2 × ℝ gauge algebra. We show how to define the boundary duals of the gravity actions using the method of non-linear realisations and suitable Inverse Higgs constraints. In particular, the non-relativistic version of the Schwarzian action is constructed in this way. We derive the asymptotic symmetries of the theory, as well as the corresponding conserved charges and Newton-Cartan geometric structure. Finally, we show how the same construction applies to the Carrollian case.
Research Interests:
We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and... more
We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré∞, and we show that it contains among others an (A)dS quotient. We discuss a non-linear realisation of this infinite-dimensional algebra, and construct a particle action based on it. The latter yields a geodesic equation that includes (A)dS curvature corrections at every order.
Research Interests:
Starting from the coadjoint Poincaré algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincaré algebra is able to induce a mechanism of... more
Starting from the coadjoint Poincaré algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincaré algebra is able to induce a mechanism of dimensional reduction between the usual coordinates of the Minkowski space and the extra-dimensional variables which turn out to form an antisymmetric tensor under the Lorentz group. Analysing the dynamics of this model, we find that, in a particular limit, it is possible to integrate out the extra variables and determine their effect on the dynamics of the material point in the usual space time. The model describes a particle in D dimensions subject to a harmonic motion when one of the parameters of the model is negative. The result can be interpreted as a modification to the flat Minkowski metric with non trivial Riemann, Ricci tensors and scalar curvature.
Research Interests:
We construct Chern-Simons gravities in (2 + 1)-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions. In the first case, there is an invariant and non-degenerate bilinear form, however... more
We construct Chern-Simons gravities in (2 + 1)-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions. In the first case, there is an invariant and non-degenerate bilinear form, however the field equations do not allow to express the spin connections in terms of the dreibeins. In the second case there is no invariant non-degenerate bilinear form. Therefore, in both cases we do not have an ordinary gravity theory. Instead, if we consider the stringy Newton-Hooke algebra with extensions as gauge group we have an invariant non-degenerate metric and from the field equations we express the spin connections in terms of the geometric fields.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
We consider a non-relativistic (NR) limit of (2 + 1)-dimensional Maxwell Chern-Simons (CS) gravity with gauge algebra [Maxwell] ⊕u(1) ⊕u(1). We obtain a finite NR CS gravity with a degenerate invariant bilinear form. We find two ways out... more
We consider a non-relativistic (NR) limit of (2 + 1)-dimensional Maxwell Chern-Simons (CS) gravity with gauge algebra [Maxwell] ⊕u(1) ⊕u(1). We obtain a finite NR CS gravity with a degenerate invariant bilinear form. We find two ways out of this difficulty: to consider i) [Maxwell] ⊕u(1), which does not contain Extended Bargmann gravity (EBG); or, ii) the NR limit of [Maxwell] ⊕u(1)⊕u(1)⊕u(1), which is a Maxwellian generalization of the EBG.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
... In other words, the conditions (4.15) on the solutions of the Ha-milton's equations of motion reduce the number of independent parame-ters from p+s to p . Let me observe that the system (~oll) plus (4.15) is not an inte-grable... more
... In other words, the conditions (4.15) on the solutions of the Ha-milton's equations of motion reduce the number of independent parame-ters from p+s to p . Let me observe that the system (~oll) plus (4.15) is not an inte-grable system of the mixed kind (see for instance LP ...