A covariant approach to gauged 2D self-dual fields

We obtain a non-Abelian version of a theory involving vector and tensor gauge fields interacting via a massive topological coupling, besides the nonminimun one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to make compatible gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case.     

The gauge theory of dislocations: conservation and balance laws

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie's infinitesimal invariance criterion we obtain conserved translational and rotational currents for the total Lagrangian made up of an elastic and dislocation part. We calculate the broken scaling current. Looking only on one part of the whole system, the conservation laws are changed into balance laws. Because of the lack of translational, rotational and dilatation invariance for each part, a configurational force, moment and power appears. The corresponding J , L and M integrals are obtained. Only isotropic and homogeneous materials are considered and we restrict ourselves to a linear theory. We choose constitutive laws for the most general linear form of material isotropy. Also we give the conservation and balance laws corresponding to the gauge symmetry and the addition of solutions. From the addition of solutions we derive a reciprocity theorem for the gauge theory of dislocations. Also, we derive the conservation laws for stress-free states of dislocations.     

Collective excitations of gluons

Three gauge invariant antisymmetric tensor fields are introduced in the nonabelian gauge theories. They are certain non-linear combinations of the conjugate field tensor and they obey O(3) algebra. An effective chiral lagrangian for these fields is derived. It describes 3 vector and 3 axial mesons with vacuum quantum numbers. The masses are generated by spontaneous restoration of Lorentz invariance.     

The Non-Perturbative Approach to the Infrared Problem in QCD at Finite Temperature

A non-perturbative approach is developed for investigation of the infrared problem in QCD at T ≠ 0 in the ghost-free axial gauge. The problem is solved by using a 3-dimensional theory within the exact Slavnov-Taylor identities and Schwinger-Dyson equations. The system of two non-linear integral equations for the structural functions of the gluon polarization tensor is obtained whose solution determines the infrared behavior of the temperature Green functions in the 4-dimensional QCD. The simplest solution of these equations which is the same as the first term of the perturbation expansion shows the presence of singularities in the gluon propagator at momenta p ∼ g²T, that cannot be eliminated by any choice of the gauge. The infrared instability of QCD at T ≠ 0 caused by these singularities is discussed.     

On gauge invariance and perturbative calculations in quantum chromodynamics

It is possible to regularize infra-red divergences of QCD by giving a mass to the gluon in such a way that the Becchi-Rouet-Stora invariance of the action is preserved. This regularization allows straightforward extension of dispersive techniques to the computation of radiative corrections to on-shell processes in QCD. Problems of gauge dependence, however, exist: care must be taken in the choice of the expansion parameter and only physically meaningful processes are gauge independent, e.g., cross sections summed over all final degenerate states.     

High temperature gluon matter in the background gauge

The polarisation tensor of gluons in high temperature QCD matter is discussed in the back-ground gauge and compared with that in the temporal axialA ₀=0 gauge. In both of these the gluon polarisation tensor alone is sufficient to give the asymptotically free sign of the QCD beta function. In the former the beta function and the imaginary part of the polarisation tensor are coupled in such a way that asymptotic freedom implies instability of plasma oscillations. In the latter, due to the non-covariance of the gauge condition, the beta function and the imaginary part are decoupled in such a way that the sign of the imaginary part corresponds to stable plasma oscillations.     

Some remarks on zeta function regularization in curved space-times

The question of to what extent zeta function regularization respects the invariances of a quantum field theory in a background gravitational field is investigated. It is shown that zeta function regularization provides a generalization to curved space-time of analytic propagator regularization which is known not to respect gauge invariance. Furthermore, a study of the regularized stress tensor of a conformally invariant scalar field indicates that both conformai and general coordinate invariance are violated.     

On Treder-Type Tetrad Theories of Gravitation II. Treder's Tetrad Theories in Linear Approximation

We consider some properties of TREDER'S tetrad theories, derived in I, using the field equations proposed by KASPER and LIEBSCHER . The linearized theory is considered, because the field energy becomes positive, if the energy of the weak field is a positive one. Using the dynamical equations, the field equations lead for the symmetric part of the field to the gauge invariant field equations in Hilbert gauge and to corresponding equations for the antisymmetric part. This means that in this approximation the dynamical equations replace the gauge invariance and the tetrad field corresponds to a mixture of tensor and scalar gravitons. We discuss possible experiments for showing the existence of scalar gravitons and limiting the free parameter of the theory.     

Slightly Bimetric Gravitation

The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan and Deser, we present such a derivation using universal coupling and gauge invariance.Next we slightly weaken the assumptions of universal coupling and gauge invariance, obtaining a larger "slightly bimetric" class of theories, in which the Euler-Lagrange equations depend only on a curved metric, matter fields, and the determinant of the flat metric. The theories are equivalent to generally covariant theories with an arbitrary cosmological constant and an arbitrarily coupled scalar field, which can serve as an inflaton or dark matter.The question of the consistency of the null cone structures of the two metrics is addressed.     

On confinement in a light-cone Hamiltonian for QCD

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fock-space amplitudes can be retrieved self-consistently from solutions in the -space. The approach is based on the novel method of iterated resolvents and on discretized light-cone quantization driven to the continuum limit. It is free of the usual perturbative Tamm-Dancoff truncations in particle number and coupling constant and respects all symmetries of the Lagrangian including covariance and gauge invariance. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fock-space regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement. Received: 27 March 1998 / Revised version: 3 June 1998 / Published online: 16 September 1998     

Gauge Theory Gravity with Geometric Calculus

A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance. A new unitary formulation of Einstein’s tensor illuminates long-standing problems with energy–momentum conservation in general relativity. Geometric calculus provides many simplifications and fresh insights in theoretical formulation and physical applications of the theory.     

Non-perturbative to perturbative QCD via the FFBRST

Recently a new type of quadratic gauge was introduced in QCD in which the degrees of freedom are suggestive of a phase of abelian dominance. In its simplest form it is also free of Gribov ambiguity. However this gauge is not suitable for usual perturbation theory. The finite field dependent BRST (FFBRST) transformation is a method established to interrelate generating functionals for different effective versions of gauge fixed field theories. In this paper we propose a FFBRST transformation suitable for transforming the theory in the new quadratic gauge into the standard Lorenz gauge Faddeev–Popov version of the effective lagrangian. The task is made interesting by the fact that the effective lagrangian is invariant under two different BRST transformations which leads to suitable extension of the previous procedures to accomplish the required result. We are thus able to identify a field redefinition to go from a non-perturbative phase of QCD to perturbative QCD.     

A statistical mechanics view of quantum chromodynamics: Lattice gauge theory

Recent developments in lattice gauge theory are discussed from a statistical mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of. QCD will be discussed and a few remarks concerning future directions of the field will be made.Supported in part by the NSF under grant No. PHY82-01948     

Hawking Radiation from Horizons of Reissner-Nordström de Sitter Black Hole with a Global Monopole via Anomalies

Hawking radiation from cosmological horizon and event horizon of the Reissner-Nordström de Sitter black hole with a global monopole is studied via a new method that was propounded by Robinson and Wilzek and elaborated by Banerjee and Kulkarni. The results show that the gauge current and energy-momentum tensor fluxes, which required keeping gauge covariance and general coordinate invariance at the quantum level in the effective field theory, are exactly equivalent to those of Hawking radiation from the event horizon and the cosmological horizon, respectively.     

The accelerated scaling attractor solution of the interacting agegraphic dark energy in Brans–Dicke theory

We study the deeply virtual Compton scattering off a spin-one particle, as the case for the coherent scattering off a deuteron target. We extend our approach, formulated initially for a spinless case, and discuss the role of twist three contributions for restoring the gauge invariance of the amplitude. Using twist three contributions and relations, which emanate from the QCD equations of motion, we derive the gauge invariant amplitude for the deeply virtual Compton scattering (DVCS) off hadrons with spin 1. Using the derived gauge invariant amplitude, the single spin asymmetry is discussed.     

Algebraic interpretation of the Yang-Mills field

Einstein's principle of general relativity is a dynamical-group approach in that all dynamics is implied by the invariance and no force is introduced (as an external, symmetry-breaking factor). In this spirit we take a Poincaré-invariant free wave equation and, deforming the Poincaré group to the de Sitter group, obtain interaction. This illustrates our algebraic approach to gauge invariance, whereby the (generalized) Maxwell tensor of the Yang-Mills field appears as structure constants of the homogeneous algebra obtained as a deformation of an inhomogeneous one, with interaction appearing via the same tensor, which plays a role corresponding to the curvature tensor in Einstein's general relativity.     

Anomalies and Hawking Radiation of NUT-Kerr-Newman de Sitter Black Hole

Hawking radiation of NUT-Kerr-Newman de Sitter black hole is studied via anomalous point of view in this paper. The results show that the charged current and energy-momentum tensor fluxes, to restore gauge invariance and general coordinate covariance at the quantum level in the effective field theory, are exactly equal to those of Hawking radiation from the event horizon (EH) and the cosmological horizon (CH) of NUT-Kerr-Newman de Sitter black hole, respectively.     

Infrared properties of two-loop,initial state spectator interactions in the Drell-Yan process

We use the light-cone axial gauge of proper-time ordered perturbation theory and study the soft-IR properties of the two-loop virtuals' diagrams considered by Bodwin, Brodsky and Lepage for ππ → μ⁺μ^- + X. It is shown that although the systematic summation over all possible spectator interactions removes the outside soft-IR divergences in the non-overlapping ladder Glauber diagrams, unphysical inside soft-IR divergences persist. So, in the light-cone axial gauge the on-shell Glauber region is not a gauge invariant concept which can be physically isolated from radiative corrections which non-trivially involve other diagrammatic regions. Due to gauge invariance it can be potentially misleading in eikonal phenomenologies based on perturbative QCD to assume an ad hoc inside soft-IR cutoff in analyzing possible non-abelian effects in multiple scatterings involving spectators.     

Gauge fixing,BRS invariance and Ward identities for randomly stirred flows

The Galilean invariance of the Navier–Stokes equation is shown to be akin to a global gauge symmetry familiar from quantum field theory. This symmetry leads to a multiple counting of infinitely many inertial reference frames in the path integral approach to randomly stirred fluids. This problem is solved by fixing the gauge, i.e., singling out one reference frame. The gauge fixed theory has an underlying Becchi–Rouet–Stora (BRS) symmetry which leads to the Ward identity relating the exact inverse response and vertex functions. This identification of Galilean invariance as a gauge symmetry is explored in detail, for different gauge choices and by performing a rigorous examination of a discretized version of the theory. The Navier–Stokes equation is also invariant under arbitrary rectilinear frame accelerations, known as extended Galilean invariance (EGI). We gauge fix this extended symmetry and derive the generalized Ward identity that follows from the BRS invariance of the gauge-fixed theory. This new Ward identity reduces to the standard one in the limit of zero acceleration. This gauge-fixing approach unambiguously shows that Galilean invariance and EGI constrain only the zero mode of the vertex but none of the higher wavenumber modes.     

Perturbative gauge invariance: electroweak theory II

A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.