Quantum Field Theory

Before going much further, given the engagement with Foucault that occupies much of the early sections of this nomadic exploration, I should address Foucault's (1972) theorizations of History in The Archaeology of Knowledge and his problematization of " the search for a total history, in which all the differences of a society might be reduced to a single form, to the organization of a world-view, to the establishment of a system of values, to a coherent type of civilization " (p. 12) therein as my reading does not fully cohere with Ball's (2013) assertion that Foucault " reject[ed]… essentialisms and universals ".

One of the key philosophical questions regarding quantum field theory is whether it should be given a particle or field interpretation. The particle interpretation of QFT is commonly viewed as being undermined by the well-known no-go results, such as the Malament, Reeh-Schlieder and Hegerfeldt theorems. These theorems all focus on the localizability problem within the relativistic framework. In this paper I would like to go back to the basics and ask the simple-minded question of how the notion of quanta appears in the standard procedure of field quantization, starting with the elementary case of the finite numbers of harmonic oscillators, and proceeding to the more realistic scenario of continuous fields with infinitely many degrees of freedom. I will try to argue that the way the standard formalism introduces the talk of field quanta does not justify treating them as particle-like objects with well-defined properties.

We study both spherically symmetric and rotating black holes with dilaton coupling, and discuss the evaporation of these black holes via Hawking's quantum radiation and their fates. We find that the dilaton coupling constant α drastically affects the emission rates, and therefore the fates of the black holes. When the charge is conserved, the emission rate from the non-rotating hole is drastically changed beyond α = 1 (a superstring theory) and diverges in the extreme limit. In the rotating cases, we analyze the slowly rotating black hole solution with arbitrary α as well as three exact solutions, the Kerr-Newman (α = 0), and Kaluza-Klein (α = √ 3), and Sen black hole (α = 1 and with axion field). Beyond the same critical value of α ∼ 1, the emission rate becomes very large near the maximally charged limit, while for α < 1 it remains finite. The black hole with α > 1 may evolve into a naked singularity due to its large emission rate. We also consider the effects of a discharge process by investigating superradiance for the non-rotating dilatonic black hole.

de Sitter space-time has a one complex parameter family of invariant vacua for the theory of a free, massive scalar field. For most of these vacua, in an interacting scalar theory the one loop corrections diverge linearly for large values of the loop momentum. These divergences are not of a form that can be removed by a de Sitter invariant counterterm, except in the case of the Euclidean, or Bunch-Davies, vacuum.

I present some recollections of the first years, in the 1980's and 1990's, of the Theoretical Physics Group of the University of Rome "Tor Vergata". I will focus on my interactions with Roberto, which were particularly intense when I was helping him with the key course on "Quantum and Statistical Mechanics" , but also on the role that he played in shaping the very structure of the group, and of the University at large.

In this work we study noncommutative Friedmann-Robertson-Walker (FRW) cosmology coupled to a scalar field endowed with an exponential potential. The quantum scenario is analyzed in the Bohmian formalism of quantum trajectories to investigate the effects of noncommutativity in the evolution of the universe.

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a non-linear differential equation, and the various solutions of such a non-linear equation represent different gauge configurations known as Gribov copies.

Following a previous work on the quantization of a massless scalar field in a spacetime representing the head on collision of two plane waves which fucus into a Killing-Cauchy horizon, we compute the renormalized expectation value of the stress-energy tensor of the quantum field near that horizon in the physical state which corresponds to the Minkowski vacuum before the collision of the waves. It is found that for minimally coupled and conformally coupled scalar fields the respective stress-energy tensors are unbounded in the horizon. The specific form of the divergences suggests that when the semiclassical Einstein equations describing the backreaction of the quantum fields on the spacetime geometry are taken into account, the horizon will acquire a curvature singularity. Thus the Killing-Cauchy horizon which is known to be unstable under "generic" classical perturbations is also unstable by vacuum polarization. The calculation is done following the point splitting regularization technique. The dynamical colliding wave spacetime has four quite distinct spacetime regions, namely, one flat region, two single plane wave regions, and one interaction region. Exact mode solutions of the quantum field equation cannot be found exactly, but the blueshift suffered by the initial modes in the plane wave and interaction regions makes the use of the WKB expansion a suitable method of solution. To ensure the correct regularization of the stress-energy tensor, the initial flat modes propagated into the interaction region must be given to a rather high adiabatic order of approximation. 0

We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, which encompasses linear optical quantum computing.

We study the renormalized energy-momentum tensor of gravitons in a de Sitter space-time. After canonically quantizing only the physical degrees of freedom, we adopt the standard adiabatic subtraction used for massless minimally coupled scalar fields as a regularization procedure and find that the energy density of gravitons in the E(3) invariant vacuum is proportional to H 4 , where H is the Hubble parameter, but with a positive sign. According to this result the scalar expansion rate, which is gauge invariant in de Sitter space-time, is increased by the fluctuations. This implies that gravitons may then add to conformally coupled matter in driving the Starobinsky model of inflation.

We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. This is applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T c turns out to be smaller than its zero temperature value.

The long-range forces that act between neutral atoms and molecules have been known as dispersion forces since the work of London, who was the first to make manifest the connection between these forces and the dispersion of light by atoms, already guessed at by Newton. The analysis and application of the analyticity properties of scattering amplitudes, developed several decades ago in the context of quantum field theory, is known as dispersion theory. In this article we review the approach to dispersion forces based on dispersion theory. We give a general discussion ofthe concept of potential in quantum field theory and then show how a study of two-photon exchange amplitudes leads to a model-independent derivation and generalization of the formulas describing retarded dispersion forces for the case of two neutral atoms, first obtained by Casimirand Polder. We then review later extensions to the interaction of a charged and a neutral system and recent work on the case where both systems are charged. The connection between the dispersion-theory approach and more conventional methods is described. We also illustrate the use of dispersion-theory techniques to study forces arising from two-neutrino exchange and two-meson exchange. The effect of dispersion forces on the energy levels of the Rydberg states of helium is briefly sketched. Finally, some open questions are mentioned.

In recent work a new order parameter has been constructed for abelian gauge theories in the presence of matter, both in the continuum and on the lattice. The order parameter directly probes whether charge is screened and enables the various Higgs phases to be distinguished. We generalize this to non-abelian gauge groups on the lattice, and analyze a specific model of an S 3 gauge theory with S~matter. In the course of our general investigation we construct a lattice operator that measures non-abelian discrete charge, and is related to a non-abelian generalization of the 't Hooft loop operator. This also provides further confirmation of the recent prediction that black holes should be able to carry discrete non-abelian quantum hair. 0550-3213/92/$05.00

Mind , the inner most box of nature has not been investigated by modern physicists . Mind has not been  incorporated in Standard model. Mind can only be studied by participatory science. Having searched Basic building blocks of the universe i.e. mass part of reality , we have also investigated mind part of reality and finally two fundamental particles with mind and mass realities  are hypothesized . Now we discuss how to further investigate mind so as to know their structures and functions. Atomic genetics is the branch of science where we investigate about fundamental interactions of the universe i.e. atomic transcription and translations . New words have been coined to understand hidden science of mind part of reality. Mind reality have been recognized as different faces by “I”  about 5000 years back  to Arjuna in Mahabharata. It is just like to understand any language through Alphabets. These are ( different faces )  Alphabets of mind reality. One Mind reality has one face identity and the second mind reality has second face identity and so on. The facial expression represents phenomenon of intelligence and different face represents different types of properties carrying  property. The open eyes means property is activated while close eye means property is inactivated. In spite of carrying properties conscious ness they also know how to conduct not only origin of universe but also how to create two different universe i.e. next creation could be different from this creation . In all, It is automatic system of the universe .  The mind realities which are  of good properties have devtas face identity ( first five faces on both side ) and those mind realities which are of bad properties have demons face identity ( last four faces on both side ) . These are named as code PCPs or messenger atomic genes . The central face is CCP  or Thought script  where all thoughts of the universe are banked . It is bank of data of all information s of the universe  It is face identity of Anti mind particles as data of all information’s of the universe are stored as anti mind particles . It is the Time mind ness ( biological clock ) that keeps on expressing different  thoughts from this thought script (CCP) . There are four more faces  ( black bodies ) shown on extreme left and right floating in fire are CPs ( translating Atomic genes) . That translates the messages and realizes it and reacts accordingly . Rest pictures are creation of different individuals and nature (sun , moon and snake and other pictures made on hands and body ) by different thoughts of Almighty B.B.B. The entire picture has been explained in Geeta in  11/ 10 and 11 .Whatever is being created in this universe is basically not by our thoughts rather it is the thought  of Almighty B.B.B ( Yang B.B.B or matter B.B.B. or Male B.B.B working as Highest center of the universe. ) that is dominated over creation and destruction of this cycle of the  universe.

In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian PT -symmetric wrong-sign quartic Hamiltonian H = 1 2 p 2 − gx 4 has the same spectrum as the conventional Hermitian HamiltonianH = 1 2 p 2 + 4gx 4 − √ 2g

Using standard coordinates, the Maxwell equations in the Reissner-Nordström geometry are written in terms of a couple of scalar fields satisfying Klein-Gordon like equations. The density of states is derived in the semi-classical approximation and the first quantum corrections to the black hole entropy is computed by using the brick-wall model. *

In this work we show that 3d Feynman amplitudes of standard QFT in flat and homogeneous space can be naturally expressed as expectation values of a specific topological spin foam model. The main interest of the paper is to set up a framework which gives a background independent perspective on usual field theories and can also be applied in higher dimensions. We also show that this Feynman graph spin foam model, which encodes the geometry of flat space-time, can be purely expressed in terms of algebraic data associated with the Poincaré group. This spin foam model turns out to be the spin foam quantization of a BF theory based on the Poincaré group, and as such is related to a quantization of 3d gravity in the limit G N → 0. We investigate the 4d case in a companion paper [1] where the strategy proposed here leads to similar results.

We derive an effective dissipative quantum field theory for fluctuating orbital currents in clean CuO2 sheets of high-Tc cuprates, based on a three-band model. The Coulomb repulsion term between Cu-and O-sites is decoupled in terms of current operators representing horizontal and vertical parts of circulating currents within each CuO2 unit cell of the lattice. The model has ordering of currents at finite temperatures. The dissipative kernel in the model is of the form |ω|/|q|, indicating Landau damping. Applications of the effective theory to other models are also discussed. PACS numbers: 74.20.Rp, 74.50.+r, Constructing an effective description of the longwavelength and low-energy physics of high-T c superconducting cuprates represents a profound and formidable problem in physics. Such a description must be consistent with experimental observations of several anomalous normal state properties of these systems. Varma has recently proposed that quantum critical fluctuations associated with the breakup of a subtle order, involving circulating currents, could induce the observed anomalous normal state properties of high-T c superconductors [1]. Essentially, the associated quantum critical fluctuations are suggested to produce a fluctuation spectrum resulting in a Marginal Fermi Liquid . Recently, such a spectrum has been derived from a conjectured effective field theory of circulating currents . It should, however, be mentioned that a recent numerical evaluation of the current-current correlations in a three-band t − J-model with 24 sites, where doubly occupied sites have been projected out, shows no evidence of the orbital current pattern proposed by Varma [4].

Negative dimensional integration method (NDIM) is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass and in the case where all of them are massless. Our results are given in terms hypergeometric functions of Mandelstam variables and for arbitrary exponents of propagators and dimension D as well.

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy based on the method of finite elements. We are able to formulate fully consistent quantum-mechanical systems directly on a lattice in terms of operator difference equations. One advantage of this discretized formulation of quantum mechanics is that the ambiguities associated with operator ordering are eliminated. Furthermore, the scheme provides an easy way in which to obtain the energy levels of the theory numerically. A generalized version of this discretization scheme can be applied to quantum field theory problems. The difficulties normally associated with fermion doubling are eliminated. Also, one can incorporate local gauge invariance in the finite-element formulation. Results for some field theory models are summarized. In particular, we review the calculation of the anomaly in two-dimensional quantum electrodynamics (the Schwinger model). Finally, we discuss nonabelian gauge theories.

The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge e is taken to be imaginary. However, if one also specifies that the potential A µ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field ϕ has a cubic self-interaction of the form iϕ 3 . The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermitian quantum electrodynamics is a particularly interesting quantum field theory model because it is asymptotically free.

The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. However, one has to check that, as well as preserving the standard cosmological equations, this does not destroy other predictions, such as the junction conditions that underlie the use of standard stellar models. We confirm that no problems arise here: hence, the Trace-Free Einstein Equations are indeed viable for cosmological and astrophysical applications.

Given a local quantum field theory net A on the de Sitter spacetime dS d , where geodesic observers are thermalized at Gibbons-Hawking temperature, we look for observers that feel to be in a ground state, i.e., particle evolutions with positive generator, providing a sort of converse to the Hawking-Unruh effect. Such positive energy evolutions always exist as noncommutative flows, but have only a partial geometric meaning, yet they map localized observables into localized observables.

Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Möbius group. We infer from this that every conformal net is normal and conormal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselsection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of PSL(2, R), showing that they violate 3-regularity for n > 2. When n ≥ 2, we obtain examples of non Möbius-covariant sectors of a 3-regular (non 4-regular) net.

We introduce duals for non-Abelian lattice gauge theories in dimension at least three by using a categorical approach to the notion of duality in lattice theories. We first discuss the general concepts for the case of a dual-triangular lattice (i.e., the dual lattice is triangular) and find that the commutative tetrahedron condition of category theory can directly be used to

Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar field φ of dimension 2 . It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra of φ is shown to coincide with a simpler one, generated by a bilocal scalar field V (x 1 , x 2 ) of dimension (1, 1) . The modes of V together with the unit operator span an infinite dimensional Lie algebra L V whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c . Wightman positivity (i.e. unitarity of the representations of L V ) is proven to be equivalent to c ∈ N .

In this article, our prime objective is to study the inflationary paradigm
from generalized tachyon (GTachyon) living on the world volume of a non-BPS string
theory. The tachyon action is considered here is getting modified compared to the
original action. One can quantify the amount of the modification via a power q
instead of 1/2 in the effective action. Using this set up we study inflation from
various types of tachyonic potentials, using which we constrain the index q within,
1/2 < q < 2, and a specific combination (∝ α
0M4
s
/gs) of Regge slope α
0
, string
coupling constant gs and mass scale of tachyon Ms, from the recent Planck 2015
and Planck+BICEP2/Keck Array joint data. We explicitly study the inflationary
consequences from single field, assisted field and multi-field tachyon set up. Specifi-
cally for single field and assisted field case we derive the results in the quasi-de-Sitter
background in which we will utilize the details of cosmological perturbations and
quantum fluctuations. Also we derive the expressions for all inflationary observables
using any arbitrary vacuum and Bunch-Davies vacuum. For single field and assisted
field case we derive-the inflationary flow equations, new sets of consistency relations.
Also we derive the field excursion formula for tachyon, which shows that assisted
inflation is in more safer side compared to the single field case to validate effective
field theory framework. Further we study the features of CMB Angular power spectrum
from TT, TE and EE correlations from scalar fluctuations within the allowed
range of q for each potentials from single field set-up. We also put constraints from
the temperature anisotropy and polarization spectra, which shows that our analysis
is consistent with the Planck 2015 data. Finally, using δN formalism we derive the
expressions for inflationary observables in the context of multi-field tachyons

The spontaneous breakdown of symmetry in this renormalizable field theory results in massive Proca bosons that act as intermediaries of the weak interactions as well as leaving one massless vector field understood to be the boson. The resulting theory is renormalizable and predicts the existence of two charged Proca boson W ± µ and one neutral Proca boson Z µ . This model uses quarks to build the hadrons and the hadrons constructed from each generation participate in both weak and strong interactions in effect realizing the universality of the weak Fermi coupling G F . In order to construct hadron with their known electric charges, the quarks must carry fractional charges. For example, suppressing their color index, the two quarks u and d form the first generation and can be expressed as a doublet

Primary Focus  Quantum Computing Architectures - Qubit-network Stabilization, Coherence and Propagation,
                          CQER (coherent quantum entanglement resonance)

Quantum computing ("QC") systems that have begun to reach the stage of experimental implementation and testing range widely from adiabatic architectures to more "classical" quantum logic gate and quantum circuit designs, emergent and promising work in topological quantum computing models, and investigations based upon quantum chaos and turbulence including trapped ions and sustainable, repeatable cascade effects on similar bases.  Fundamental challenges exist in the areas of noise mitigation and stabilization of qubit networks (arrays) during the sustained period of times required to complete algorithm processing.  The "QC problem" is critical for all current qubit and system-level designs and impacts the application of QC for real-world application tasks.  My research beginning in quantum and relativity theory has been directed increasing at solving this “QC problem” of stabilization, sustainability and consistent reproducible measurement.

Stabilization and maintainenance of qubit-network coherence is a current impasse barrier that must be overcome in order for QC to evolve into systems that can provide reliable and stable performance for different classes of problems and for performance over time and in diverse physical operating environments.  Propagation of coherent "quantum geometries/topologies" from one region of a closed system to another, or between QC systems, is another critical issue, one in which investigations turns to biology and also fluid dynamics as a high-possibility for illumination and inspiration for solutions.

In addition, many of the other scientific investigations in diverse fields - physics, astrophysics, molecular biology, epigenetics, nanostructured materials, to name a few - can arguably be said to certainly benefit from (if not require) QC in order to progress from "present early/speculative theory stages" to mature theory, practical experimental validation, and useful applications.  This is arguably the case also for certain critical optimization, search and decision problems of international security, public health, environmental management and crisis response, space exploration, and also novel energy generation and power technologies.

Current attention is strongly directed at defining physical and algorithmic methods that can employ an "inverse" model of how noise and decoherence is used.  This moves away from classical "Turing computing machine" concepts and closer to biology, and specifically the coherent propagation of information in both neuro-motor communications and the immune system.  "Noise" - the disrupter of QC - may actually be translatable into cybernetic value for control, modulation, and stabilization, removing the need for complex and unwieldy error-correction qubit arrays and opening the gateway to very large scale interactions among independent qubit entanglement sets. The area of investigation known as CQER is of particular interest for not only QC per se but also the implications for quantum relativity and gravity as well as the implications and derivations of the same for both the Standard Model and Cosmology.  Recent work also includes a fractal recursive computational model and its expectations for physical implementation using cellular-type field arrays that incorporate BEC (Bose-Einstein Condensate) properties.

Single Field Theory (SOFT) utilizes a modified Einstein-Kaluza macroscopically extended five-dimensional space-time continuum to unify gravity, electromagnetism and the quantum. Our experiential four-dimensional space-time continuum is essentially a ‘sheet’ with a quantized ‘effective width’ in the fifth space-like embedding dimension.  Since material particles are nothing more than various forms of quantized extrinsic curvature of the ‘sheet’, all normal matter is limited to a three-dimensional spatial existence. The normal primary ‘sheet’ that constitutes our three-dimensional space of experience and sensation corresponds to the principle quantum of n=1. The power and utility of this model is such that it can explain such diverse enigmatic observations as wave/particle duality as well as unify the seemingly incompatible shell and fluid models of the nucleus into one single picture.

This paper touches on the subject of whether light really needs a medium, which is termed the luminiferous ether, for its transmission as is in the case of sound which requires a fluid such as air or liquid as the medium for its transmission, and the subject of the velocity of light.

"We start from the Einstein-Hilbert action for the gravitational field in the presence of a “point particle” source, and cast the action into the corresponding phase space form. The dynamical variables of such a system satisfy the point particle mass shell constraint, the Hamilton and the momentum constraints of the canonical gravity. In the quantized theory, those constraints become operators that annihilate a state. A state can be represented by a wave functional $\psi$ that simultaneously satisfies the Klein-Gordon and the Wheeler-DeWitt- Schr¨odinger equation. The latter equation, besides the term due to gravity, also contains the Schr¨odinger like term, namely the derivative of $\psi$ with respect to time, that occurs because of the presence of the point particle. The particle’s time coordinate, $X^0$, serves the role of time. Next, we generalize the system to p-branes, and find out that for a quantized spacetime filling brane there occurs an effective cosmological constant, proportional to the expectation value of the brane’s momentum, a degree of freedom that has two discrete values only, a positive and a negative one. This mechanism could be an explanation for the small cosmological constant that drives the accelerated expansion of the universe."

Off-shellness and inhomogeneities are in the non-equilibrium dynamics of the lambda phi4 model are studied using the closed timepath formalism reformulated as kinetic field theory. We take into account initial correlations up to the 4-point functions. The model is shown to exhibit a SO(1,1) symmetry broken by interactions and initial conditions. The divergence of the corresponding Noethercurrent is calculated and the Ward-Takahashi relations for the broken symmetry are given. They constitute a set of generalized integrated kinetic equations for the general n-point functions. We demonstrate that energy-momentum conservation follows from the transport equations. As an application we discuss inhomogeneities and general non-equilibrium conditions in the free field model. In our solution we identify the casimir-effect.