Reducible Gauge Theories Research Articles

Noether's second theorem in a general setting: reducible gauge theories

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge symmetries and Noether's identities are formulated, and their equivalence by means of certain intertwining operator is proved.

BRST approach to Lagrangian construction for fermionic massless higher spin fields

We develop the BRST approach to Lagrangian formulation for all massless half-integer higher spin fields on an arbitrary dimensional flat space. General procedure of Lagrangian construction describing the dynamics of fermionic field with any spin is given. It is shown that in fermionic case the higher spin field model is a reducible gauge theory and the order of reducibility grows with the value of spin. No off-shell constraints on the fields and the gauge parameters are used. We prove that in four dimensions after partial gauge fixing the Lagrangian obtained can be transformed to Fang–Fronsdal form however, in general case, it includes the auxiliary fields and possesses the more gauge symmetries in compare with Fang–Fronsdal Lagrangian. As an example of general procedure, we derive the new Lagrangian for spin 5 / 2 field containing all set of auxiliary fields and gauge symmetries of free fermionic higher spin field theory.

ASSOCIATIVITY AND OPERATOR HAMILTONIAN QUANTIZATION OF GAUGE THEORIES

We show that the associative algebra structure can be incorporated in the BRST quantization formalism for gauge theories such that extension from the corresponding Lie algebra to the associative algebra is achieved using operator quantization of reducible gauge theories. The BRST differential that encodes the associativity of the algebra multiplication is constructed as a quadratic second-order differential operator on the bar resolution.

Dynamical chiral symmetry breaking on a brane in reduced QED

Reduced gauge theories are theories in which while gauge fields propagate in a bulk, fermion fields are localized on a brane. We study dynamical chiral symmetry breaking on a 2-brane and a 1-brane in reduced QED_{3+1}, and on a 1-brane in reduced QED_{2+1}. Since, unlike higher dimensional gauge theories, QED_{3+1} and QED_{2+1} are well defined, their reduced versions can serve as a laboratory for studying dynamics in a higher dimensional brane world. The analysis of the Schwinger-Dyson (SD) equations in these theories reveals rich and quite nontrivial dynamics in which the conformal symmetry and its breakdown play a crucial role. Explicit solutions of the SD equations in the near-critical regime are obtained and the character of the corresponding phase transition is described.

Topologically massive abelian gauge theory from BFT Hamiltonian embedding of a first-order theory

We start with a new first-order gauge non-invariant formulation of massive spin-1 theory and map it to a reducible gauge theory, viz. abelian B∧ F theory by the Hamiltonian embedding procedure of Batalin, Fradkin and Tyutin (BFT). This equivalence is shown from the equations of motion of the embedded Hamiltonian. We also demonstrate that the original gauge non-invariant model and the topologically massive gauge theory can both be obtained by a suitable choice of gauges, from the phase space partition function of the embedded Hamiltonian, proving their equivalence. A comparison of the first-order formulation with the other known massive spin-1 theories is also discussed.

The osp(1,2)-covariant Lagrangian quantization of reducible massive gauge theories

The osp(1,2)-covariant Lagrangian quantization of irreducible gauge theories is generalized to L-stage reducible theories. The dependence of the generating functional of Green’s functions on the choice of gauge in the massive case is discussed and Ward identities related to osp(1,2) symmetry are given. Massive first-stage theories with closed gauge algebra are studied in detail. The generalization of the Chapline–Manton model and topological Yang–Mills theory to the case of massive fields are considered as examples.

IRREDUCIBLE ANTIFIELD BRST–ANTI-BRST FORMALISM FOR REDUCIBLE GAUGE THEORIES

In this paper we develop an irreducible antifield BRST–anti-BRST formalism for reducible gauge theories.

Irreducible antifield-BRST approach to reducible gauge theories

An irreducible antifield BRST quantization method for reducible gauge theories is proposed. The general formalism is illustrated in the case of the Freedman-Townsend model.

Finite Yang-Mills integrals

We use Monte Carlo methods to directly evaluate D-dimensional SU( N) Yang-Mills partition functions reduced to zero Euclidean dimensions, with and without supersymmetry. In the non-supersymmetric case, we find that the integrals exist for D=3, N≥4 and D=4, N≥3 and, lastly, D≥5, N≥2. We conclude that the D=3 and D=4 integrals exist in the large N limit, and therefore lead to a well-defined, new type of Eguchi-Kawai reduced gauge theory. For the supersymmetric case, we check, up to SU(5), recently proposed exact formulas for the D=4 and D=6 D-instanton integrals, including the explicit form of the normalization factor needed to interpret the integrals as the bulk contribution to the Witten index.

Wess-Zumino terms for reducible anomalous gauge theories

Reducible off-shell anomalous gauge theories are studied in the framework of an extended Field-Antifield formalism by introducing new variables associated with the anomalous gauge degrees of freedom. The Wess-Zumino term for these theories is constructed and new gauge invariances appear. The quantum effects due to the extra variables are considered.

Path integral and solutions of the constraint equations: the case of reducible gauge theories

It is shown that the BRST path integral for reducible gauge theories, with appropriate boundary conditions on the ghosts, is a solution of the constraint equations. This is done by relating the BRST path integral to the kernel of the evolution operator projected on the physical subspace.

The physical phase of dimensionally reduced gauge theories

We investigate the relationship between the high-temperature deconfined phase of the SU(2) gauge theory to the phases of the corresponding three-dimensional adjoint Higgs model. For various temperatures we simulate the effective theory in a neighbourhood of the physical states, that is of those values of the coupling constants that describe the infrared behaviour of the four-dimensional theory and which have been calculated by applying dimensional reduction techniques. We show that the physical points belong to the confined phase of the SU(2) adjoint Higgs model.

On the quantization of reducible gauge systems

Reducible gauge theories with constraints linear in the momenta are quantized. The equivalence of the reduced phase space quantization, Dirac quantization, and BRST quantization is established, provided one transforms appropriately the Dirac wave functions under changes of representation of the constraint surface and of the reducibility functions. The ghosts of ghosts are found to play a crucial role in the equivalence proof.

OFF-SHELL NILPOTENCY FOR ON-SHELL REDUCIBILITY

The direct way of Lagrangian BRS gauge-fixing we proposed recently is applied to reducible gauge theories; antisymmetric tensor gauge theories are considered as definite examples. It enables us to do without ad hoc ghosts for ghosts. It also achieves BRS-exact forms of full gauge-fixing terms by means of off-shell nilpotent BRS transformations.

A BRST lagrangian quantization of reducible gauge theories: Non-abelianp-forms and string field theories

By a suitable deformation of the reducible BRST algebra of the Abelianp-forms we obtain an explicit nilpotent BRST for the corresponding open reducible non-Abelianp-forms theory. We consider the Freedman-Townsend model and the corresponding (topological) massless limit. This allows us to perform a standard BRST quantization of the theory which avoids the Batalin-Vilkovisky formalism. This procedure leads to the introduction of auxiliary fields (related to BV antifields) which assume a universal form in terms of a single object belonging to the universal enveloping algebra. The auxiliary fields are interpreted as a sort of connection. A formal extension to the case of string field theory is presented.

Is the Stochastic Gauge-Fixing a Consistent Method for Reducible Gauge Theories?

By using the Stochastic Gauge-Fixing term derived in a previous paper, we stochastically quantize the Non-Abelian Antisymmetric Tensor Field theory as an example of the Reducible Gauge Theories. Though all the quantities are finitely computed and the induced vertex really reproduces the full ghost contributions, the uninterpretable terms still remain.

Is the Stochastic Gauge-Fixing a Consistent Method for Reducible Gauge Theories?

Is the Stochastic Gauge-Fixing a Consistent Method for Reducible Gauge Theories?

STOCHASTIC GAUGE-FIXING FOR NON-ABELIAN ANTISYMMETRIC TENSOR FIELDS

By using the BRST invariance, we find the stochastic gauge-fixing function which corresponds to the ordinary gauge-fixing function for non-Abelian antisymmetric tensor fields as reducible gauge theories. Then the trial stochastic gauge-fixing function is obtained perturbatively.

Stochastic Quantization of Non-Abelian Antisymmetric Tensor Fields

We study the stochastic quantization of Non-Abelian Antisymmetric Tensor Fields as Reducible Gauge Theories. Then we prove that the fictitious time divergent longitudinal component reproduces the so-called Faddeev-Popov ghost effects from 1-loop contributions

Some aspects of the quantization ofp-forms and reducible gauge theories

The quantization of thep-form inD dimensions is carried out according to both an extension of the BRST formalism and a method due to A. S. Schwarz. The latter yields a suggestive interpretation of the role of nonphysical fields in the quantization of reducible gauge theories. The introduction of gauge conditions of a different type (namely self-dual) modifies the ghost spectrum but does not affect the partition function.