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The Batalin-Vilkovisky formalism has been used to obtain a covariant quantization of Siegel's superparticle, which is completely gauge fixed. The BRST transformations and the BRST charge are given also.

According to Dirac’s prescription the generator of gauge transformations for a constrained system endowed with primary and secondary first class constraints is constructed as a linear combination of all these (first class) constraints. Using the total Hamiltonian to generate the dynamics of the system it is shown that the time evolution of the coefficients of the secondary constraints in the generator of gauge transformations is not independent but is determined by the coefficients of the primary constraints. This result is applied to some physically interesting systems.

It is shown that the covariant action for induced 2D gravity is defined by the action of WZNW type with the U(1) Chern-Simons multivalued functional. In the light-cone gauge it coincides with Polyakov's result. The explicit SL(2, R ) current algebra structure in chiral gauge is revealed.

The precise relation between the gauge transformations in lagrangian and hamiltonian form is derived for any gauge theory. It is found that in order to define a lagrangian gauge symmetry, the coefficients of the first class constraints in the hamiltonian generator of gauge transformations must obey a set of differential equations. Those equations involve, in general, the Lagrange multipliers. Their solution contains as many arbitrary functions of time as there are primary first class constraints. If n is the number of generations of constraints (primary, secondary, tertiary…), the arbitrary functions appear in the general solution together with their successive time derivatives up to order n −1. The analysis yields as by-products: (i) a systematic way to derive all the gauge symmetries of a given lagrangian; (ii) a precise criterion for counting the physical degrees of freedom of a gauge theory directly from the form of gauge transformations in lagrangian form. This last part is illustrated by means of examples. The BRST analog of the counting of physical degrees of freedom is also discussed.

The variational methods of classical field theory may be applied to any theory with an action that is invariant under local gauge transformations. What is the significance of the resulting Noether current? This article examines such currents for both Abelian and non‐Abelian gauge theories and provides an explanation for their form and limited range of physical significance on a level accessible to those with a basic knowledge of classical field theory. Several of the more subtle aspects encountered in the application of the residual local gauge symmetry found by Becchi, Rouet, Stora, and Tyutin are also considered in detail in a self‐contained manner.

A geometrical treatment of the gauge coupling constant is proposed in terms of a generalized connection form using fibre-bundle language. This extends the notion of the coupling constant to a notion of a field. The reduction of a curvature form for the generalized connection form is described in the case of a reduction of a structure group G to a subgroup H (broken gauge symmetry), and a coupling constant for the gauge group H is constructed from the corresponding one for the gauge group G.

The author studies two-dimensional massless chiral QCD in a gauge invariant formulation. The Faddeev-Popov procedure is used to obtain a gauge invariant effective action after bosonisation, which is then quantised canonically using Dirac's prescription for constrained systems. The gauge current algebra is deduced and covariant current conservation is shown by means of the equations of motion of the bosonic matter fields.

For a closed subgroup H H of a locally compact group G G , it is shown that a covariant system ( G , A ) (G,A) is induced from a covariant system ( H , D ) (H,D) if (and only if) there exists a continuous G G -equivariant map φ : Pr im A → G / H \varphi :\Pr {\text {im}}A \to G/H .

A slight change of emphasis, from geometry towards local symmetry, provides a better framework for the formulation of gauge theories of the gravitational type. General Relativity no longer requires any improvisation, whether the local algebra is based on Poincare or on De Sitter. Application to the graded super Minkowski manifold, with local algebra based on the super Poincare algebra, leads to an action principle. The torsion constraints are obtained by straightforward variation of the action. The comparison with component supergravity has not yet been completed, but preliminary indications strongly indicate a close relationship. Local symmetry of the action principle is maintained, the structure is field independent, and the torsion constraints also preserve the local symmetry algebra. The coupling to matter shows that these constraints are necessary for the exclusion of ghosts from the matter sector.

The gauge field figures as a key concept in the modern theory of fundamental physical fields. Various deep and intimate relationships between the gauge field theory proper and the methods of differential geometry of fibered spaces have been recognized for a long time. Usually, such relationships are established in terms of group fibrations such that the fibres are implied to be some of Lie groups (see, e.g., [1–4]). In the present servey-article, which extends basic tools elaborated in the preceding publications [5, 6], the author makes an attempt to reach a higher step of gauge generality by getting over the proper Yang-Mills ansatz that the group character of the fibre must be a steed concept from the very beginning. Instead, it looks quite accessible to begin the gauge analysis with more primary starting point where some appropriate, and motivated in a physical sense, geometrical space is treated as a fibre. Such a generalized program proves to be quite feasible if the notion of diffeomorphisms of fibres in themselves is invoked to serve as the required generalized gauge transformations. Such way of extending the gauge transformation concept seems to be sufficiently natural and fundamental for all.

The explicit forms of the metric as well as the equations of motion in the first-order post-Newtonian approximation are worked out under several gauge conditions. It is noted that the so-called EIH (Einstein, Infeld, and Hoffman) equation of motion for an assembly ofN finite mass points mutually interacting via gravitation is identically obtained under three different gauge conditions, namely the harmonic gauge, Chandrasekhar gauge and a composite Chandrasekhar gauge used by Misneret al. (1970), even though the solutions for the metric are found to be all different. In one case the metric has a component apparently diverging, but finally generates regular affine connections so that the equations of motions become free from any singularity. By use of the Chandrasekhar gauge and his formulation, the second-order contribution to the acceleration of planets in the limit of test particle motion around the Sun has been calculated, the inclusion of which in the EIH set of the equations of motion would extend the relative accuracy of computing the total acceleration of any planet to better than one part in 1017.

We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of a generalization of the concept of Killing vectors and tensors in differential geometry. We apply the formalism to the motion of classical charges in abelian and non-abelian monopole fields, Comment: 15 pages, no figures

Two-dimensional quantum fields in electric and gravitational backgrounds can be described by conformal field theories, and hence all the physical (covariant) quantities can be written in terms of the corresponding holomorphic quantities. In this paper, we first derive relations between covariant and holomorphic forms of higher-spin currents in these backgrounds, and then, by using these relations, obtain higher-spin generalizations of the trace and gauge (or gravitational) anomalies up to spin 4. These results are applied to derive higher-moments of Hawking fluxes in black holes in a separate paper arXiv:0710.0456., Comment: 23 pages

We present a formalism to determine the imaginary part of a general chiral model in the derivative expansion. Our formalism is based on the worldline path integral for the covariant current that can be given in an explicit chiral and gauge covariant form. The effective action is then obtained by integrating the covariant current, taking account of the anomaly., Comment: 33 pages, minor changes, published version

We briefly recall the main steps by which we suggest to found quantum mechanics and gauge field theories on the principle of relativity, once it is extended to scale transformations of the reference system. The wave functions are constructed as consequences of the nondifferentiability of a continuous space‐time, while the Schrodinger and Dirac equations are obtained from its geodesics equations. In this framework, the gauge fields emerge as manifestation of the fractal geometry, and the gauge charges as the conservative quantities which are built from its internal symmetries.

The most general covariant gauge fixing Lagrangian is considered for a spin-two gauge theory in the context of the Faddeev-Popov procedure. In general, five parameters characterize this gauge fixing. Certain limiting values for these parameters give rise to a spin-two propagator that is either traceless or transverse, but for no values of these parameters is this propagator simultaneously traceless and transverse. Having a traceless-transverse (TT) propagator ensures that only the physical degrees of freedom associated with the tensor field propagate, and hence it is analogous to the Landau gauge in electrodynamics. To obtain such a traceless-transverse propagator, a gauge fixing Lagrangian which is not quadratic must be employed; this sort of gauge fixing Lagrangian is not encountered in the usual Faddeev-Popov procedure. It is shown that when this non-quadratic gauge fixing Lagrangian is used, two Fermionic and one Bosonic ghost arise. As a simple application we discuss the energy-momentum tensor of the gravitational field at finite temperature., Comment: 8 pages, 4 figures. Revised version to be published in Physical Review D

The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. The covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for noncommutative theories., Comment: 16 pages

The generally covariant treatment of QFT discussed in this paper is based on the first principle that ensures equivalence of observable algebras based on isometric regions of different space-times. That’s all one needs to proceed, at the conceptual level. Important developments are those connected to the works of Hollands and Wald, Verch, Hollands, Ruzzi, and one easily foresees applications of the framework to interesting situations, such as those related to AdS space-time, or in general theories on space-times with boundaries, to the exploitation of the renormalization group at the algebraic level and its possible use towards a clarification of the role of the conformal anomaly in the treatment of theories on asymptotically AdS space-times. Another, perhaps more important topic, is that related to background independent formulation of perturbative quantum gravity. We hope to report on these soon.

We consider the covariant quantization of generalized abelian gauge theories on a closed and compact n-dimensional manifold whose space of gauge invariant fields is the abelian group of Cheeger-Simons differential characters. The space of gauge fields is shown to be a non-trivial bundle over the orbits of the subgroup of smooth Cheeger-Simons differential characters. Furthermore each orbit itself has the structure of a bundle over a multi-dimensional torus. As a consequence there is a topological obstruction to the existence of a global gauge fixing condition. A functional integral measure is proposed on the space of gauge fields which takes this problem into account and provides a regularization of the gauge degrees of freedom. For the generalized p-form Maxwell theory closed expressions for all physical observables are obtained. The Greens functions are shown to be affected by the non-trivial bundle structure. Finally the vacuum expectation values of circle-valued homomorphisms, including the Wilson operator for singular p-cycles of the manifold, are computed and selection rules are derived., Comment: 23 pages

On the basis of the general principles of a gauge field theory, the gauge theory for the Poinca\ifmmode \acute{r}\else \'{r}\fi{}e-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions of true gauge fields: Lorentzian, translational, and dilatational ones. The equations for gauge fields are obtained. Geometrical interpretation of the theory is developed demonstrating that as a result of localization of the Poincar\'e-Weyl group the space-time becomes a Weyl-Cartan space. The geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is also proposed.

Even though the energy carried by a gravitational wave is not itself gauge invariant, the interaction with a gravitational antenna of the gravitational wave which carries that energy is. It therefore has to be possible to make some statements which involve the energy which are in fact gauge invariant, and it is the objective of this paper to provide them. In order to develop a gauge invariant treatment of the issues involved, we construct a specific action for gravitational fluctuations which is gauge invariant to second perturbative order. Then, via variation of this action, we obtain an energy-momentum tensor for perturbative gravitational fluctuations around a general curved background whose covariant conservation condition is also fully gauge invariant to second order. Contraction of this energy-momentum tensor with a Killing vector of the background conveniently allows us to convert this covariant conservation condition into an ordinary conservation condition which is also gauge invariant through second order. Then, via spatial integration we are able to obtain a relation involving the time derivative of the total energy of the fluctuation and its asymptotic spatial momentum flux which is also completely gauge invariant through second order. It is only in making the simplification of setting the asymptotic momentum flux to zero that one would actually lose manifest gauge invariance, with only invariance under those particular gauge transformations which leave the asymptotic momentum flux zero then remaining. However, if one works in an arbitrary gauge where the asymptotic momentum flux is non-zero, the gravitational wave will then deliver both energy and momentum to a gravitational antenna in a completely gauge invariant manner, no matter how badly behaved at infinity the gauge function might be., Comment: 13 pages, revtex4. Final version. To appear in Phys. Rev. D

Using the manifestly covariant spectator theory, and modeling the nucleon as a system of three constituent quarks with their own electromagnetic structure, we show that all four nucleon electromagnetic form factors can be very well described by a manifestly covariant nucleon wave function with zero orbital angular momentum. Since the concept of wave function depends on the formalism, the conclusions of light-cone theory requiring nonzero angular momentum components are not inconsistent with our results. We also show that our model gives a qualitatively correct description of deep inelastic scattering, unifying the phenomenology at high and low momentum transfer. Finally we review two different definitions of nuclear shape and show that the nucleon is spherical in this model, regardless of how shape is defined., 20 pages and 10 figures; greatly expanded version with new fits and discussion of DIS; similar to published version

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincar\'e invariance and parity non-invariance, we classify all the nontrivial perturbative deformations of the abelian gauge algebra. In space-time dimensions $n=3$ and $n=5$, deformations of the free theory are obtained which make the gauge algebra non-abelian and give rise to nontrivial cubic vertices in the Lagrangian, at first order in the deformation parameter $g$. At second order in $g$, consistency conditions are obtained which the five-dimensional vertex obeys, but which rule out the $n=3$ candidate. Moreover, in the five-dimensional first order deformation case, the gauge transformations are modified by a new term which involves the second de Wit--Freedman connection in a simple and suggestive way., Comment: 27 pages, 1 table, revtex4, typos corrected

We study the non-perturbative production of gluon pairs from a constant SU(3) chromo-electric background field via the Schwinger mechanism. We fix the covariant background gauge with an arbitrary gauge parameter \alpha. We determine the transverse momentum distribution of the gluons, as well as the total probability of creating pairs per unit space time volume. We find that the result is independent of the covariant gauge parameter \alpha used to define arbitrary covariant background gauges. We find that our non-perturbative result is both gauge invariant and gauge parameter \alpha independent., Comment: Final version, To be published in Physical Review D

The gauge principle is the guiding principle of the general program started by Einstein for the geometrization of fundamental interactions. By demanding the invariance of the theory under local coordinate transformations, the relevant fields carrying these interactions appear naturally as non trivial geometrical structures of the corresponding fiber bundles over space-time. In this talk we present a work in progress concerning the study of the geometrical structure and quantization of Yang-Mills theories by using what we have called an extended gauge principle. The three fundamental geometrical components of a Yang-Mills theory -the gauge fields, the gauge fixing and the ghost fieldsare unified in a new geometrical object: an extended connection in a properly chosen principal bundle. In order to construct this extended connection it is necessary to generalize the gauge fixing by using a gauge fixing connection instead of the usual local sections. A fundamental difference is that the gauge fixing connection is globally well defined even when the topology of the fiber bundle is not trivial (Gribov’s obstruction). From the equations for the curvature of the extended connection we derive the corresponding BRST transformations without imposing the usual “flatness” conditions. We show that it is possible to follow the Faddeev-Popov method in order to find the gauge fixed action corresponding to the generalized gauge fixing. 1

In the limit of infinite Newton constant, the dimensional vacuum Einstein equations reduce to their 'velocity dominated' counterparts. We construct all solutions with generic initial data and spatially closed sections by employing the constant mean curvature (CMC) gauge [1]. The latter is a nonlinearly admissible gauge in which the evolution equations are integrable ordinary differential equations and the diffeomorphism constraint decouples from the Hamiltonian constraint. The dynamical fields in this gauge are invariant under all gauge transformations but time independent spatial diffeomorphisms. The decoupled constraints are solved using a lapse-weighted conformal-traceless decomposition and produce equivalence classes of physical configurations modulo spatial diffeomorphisms. The CMC gauge can be augmented by a gauge condition on the unimodular part of the spatial metric to provide a complete gauge fixing. Based on it a complete set of fully gauge invariant dynamical fields (observables) is constructed. By utilizing an algebraic gauge condition a variant of the construction is found that isolates the physical degrees of freedoms algebraically.

In the limit of infinite Newton constant the dimensional Einstein–Hilbert action reduces to that of a nonlinear sigma-model where spatial points are coupled merely by shift terms giving rise to a diffeomorphism constraint. The full group of diffeomorphisms is shown to act non-tensorially as a gauge group on the action and the field equations. This is used to establish the admissibility as a gauge condition of the combined constant mean curvature (CMC) and zero shift conditions for spatially closed hypersurfaces. This 'CMC gauge' eventually allows for a concise isolation of the gauge invariant and physical degrees of freedoms. Here we utilize the CMC gauge to obtain a complete set of dynamical fields which are invariant under all gauge transformations but time independent spatial diffeomorphisms.

An attempt to define precise Feynman rules for theories of gauge fields in axial gauges is made by requiring consistency with theories in covariant gauges. The Wilson line operators are used to construct a modified fermion propagator which is invariant under a restricted class of gauge transformations comprising the ones that relate axial to some covariant gauge. Calculating the modified fermion propagator in the axial gauge with the Cauchy principal value prescription for spurious singularities of the gauge field propagator and with the Landshoff's prescription, it is found to one-loop order that at least one of the prescriptions is not consistent with covariant gauge Feynman rules.

As a first approach to the study of classical solutions for gauge theories in dimensions higher than four we study linear relations among the fields which ensure the equation of motion as a consequence of the Bianchi identities. We show how these relations can be obtained as integrability conditions on linear covariant first order equations. Using spherical symmetry we exhibit specific solutions of. these relations. We also hint at an algebraic approach of the ADHM type to obtain more general solutions at least in principle.

We show that the renormalisation of the N=1 supersymmetric gauge theory when working in the component formalism, without eliminating auxiliary fields and using a standard covariant gauge, requires a non-linear renormalisation of the auxiliary fields., 9 pages, including 4 figures. Plain TeX. Uses Harvmac and epsf; reference added and minor changes to Introduction

An almost-stationary gauge condition is proposed with a view to Numerical Relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is derived by a variational principle, by minimizing the deviations from isometry. The corresponding almost-stationary gauge condition allows one to put the field equations in hyperbolic form, both in the free-evolution ADM and in the Z4 formalisms., Talk presented at the Spanish Relativity Meeting, September 6-10 2005 Revised version

We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between the canonical and covariant variables are determined through a consistent account of all components of the Berry connection. The Jacobian of the canonical-to-covariant-variables transformation describes the nonconservation of the 'naive' phase space volume in the covariant coordinates (D.Xiao, J.Shi, and Q.Niu, Phys. Rev. Lett. 95, 137204 (2005))., 3 pages, to appear in Physics Letters A

We present a formalism to study the metric perturbations of the Schwarzschild spacetime. The formalism is gauge invariant, and it is also covariant under two-dimensional coordinate transformations that leave the angular coordinates unchanged. The formalism is applied to the typical problem of calculating the gravitational waves produced by material sources moving in the Schwarzschild spacetime. We examine the radiation escaping to future null infinity as well as the radiation crossing the event horizon. The waveforms, the energy radiated, and the angular-momentum radiated can all be expressed in terms of two gauge-invariant scalar functions that satisfy one-dimensional wave equations. The first is the Zerilli-Moncrief function, which satisfies the Zerilli equation, and which represents the even-parity sector of the perturbation. The second is the Cunningham-Price-Moncrief function, which satisfies the Regge-Wheeler equation, and which represents the odd-parity sector of the perturbation. The covariant forms of these wave equations are presented here, complete with covariant source terms that are derived from the stress-energy tensor of the matter responsible for the perturbation. Our presentation of the formalism is concluded with a separate examination of the monopole and dipole components of the metric perturbation., Comment: 21 pages

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time.

We analyze the mixing of the scalar glueball with the scalar-isoscalar quarkonia states above 1 GeV in a non-local covariant constituent approach. Similarities and differences to the point-particle Klein-Gordon limit and to the quantum mechanical case are elaborated. Model predictions for the two-photon decay rates in the covariant mixing scheme are indicated., 28 pages, 6 figures

Commutative supersymmetric Yang-Mills is known to be renormalizable for ${\cal N} = 1, 2$, while finite for ${\cal N} = 4$. However, in the noncommutative version of the model (NCSQED$_4$) the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of NCSQED$_4$ by working systematically within the covariant superfield formulation. In the Landau gauge, it has already been shown for ${\cal N} = 1$ that the gauge field two-point function is free of harmful UV/IR infrared singularities, in the one-loop approximation. Here we show that this result holds without restrictions on the number of allowed supersymmetries and for any arbitrary covariant gauge. We also investigate the divergence structure of the gauge field three-point function in the one-loop approximation. It is first proved that the cancellation of the leading UV/IR infrared divergences is a gauge invariant statement. Surprisingly, we have also found that there exist subleading harmful UV/IR infrared singularities whose cancellation only takes place in a particular covariant gauge. Thus, we conclude that these last mentioned singularities are in the gauge sector and, therefore, do not jeopardize the perturbative expansion and/or the renormalization of the theory.

Perturbation theory is an important tool to describe the properties of QCD at very high temperatures. Recently a new technique has been proposed to compute the one-loop effective action of QCD at finite temperature by making a gauge covariant derivative expansion, which is fully consistent with topologically small and large gauge transformations (also time dependent transformations). This technique is based on the heat kernel expansion, and the thermal Wilson line plays an essential role. We consider a general SU(N_c) gauge group., Comment: 3 pages, no figures. Proceedings for IX Hadron Physics and VII Relativistic Aspects of Nuclear Physics, Angra dos Reis, Rio de Janeiro, March 28 - April 03, 2004

We derive the fermionic contribution to the 1-loop effective action for A_4 and A_i fields at high temperatures, assuming that gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4., RevTex 4, 11 pages, 3 figures. Version 2: Typos corrected; magnetic fields restricted to parallel sector. Version accepted for publication in PRD

Nonlinear covariant parity-violating deformations of free spin-two gauge theory are studied in n>2 spacetime dimensions, using a linearized frame and spin-connection formalism, for a set of massless spin-two fields. It is shown that the only such deformations yielding field equations with a second order quasilinear form are the novel algebra-valued types in n=3 and n=5 dimensions already found in some recent related work concentrating on lowest order deformations. The complete form of the deformation to all orders in n=5 dimensions is worked out here and some features of the resulting new algebra-valued spin-two gauge theory are discussed. In particular, the internal algebra underlying this theory on 5-dimensional Minkowski space is shown to cause the energy for the spin-two fields to be of indefinite sign. Finally, a Kaluza-Klein reduction to n=4 dimensions is derived, giving a parity-violating nonlinear gauge theory of a coupled set of spin-two, spin-one, and spin-zero massless fields., 17 pages

Gauge field theory of MacDowell and Mansouri is modified using the Poincare group as Gauge group of flat Minkowski space-time.