scholarly journals GAUGE MODELS IN MODIFIED TRIPLECTIC QUANTIZATION

2001 ◽  
Vol 16 (26) ◽  
pp. 4297-4319 ◽  
Author(s):  
B. GEYER ◽  
P. M. LAVROV ◽  
P. YU. MOSHIN
Keyword(s):  
2D Gravity ◽  
Brst Symmetry ◽  
Antisymmetric Tensor ◽  
Explicit Solutions ◽  
Tensor Fields ◽  
Gauge Models ◽  
Gauge Fixing ◽  
Quantum Action

The modified triplectic quantization is applied to several well-known gauge models: the Freedman–Townsend model of non-Abelian antisymmetric tensor fields, W2 gravity, and 2D gravity with dynamical torsion. For these models we obtain explicit solutions of those generating equations that determine the quantum action and the gauge-fixing functional. Using these solutions, we construct the vacuum functional, determine the Sp(2)-invariant effective actions and obtain the corresponding transformations of extended BRST symmetry.

scholarly journals On gauge independence for gauge models with soft breaking of BRST symmetry

2014 ◽  
Vol 29 (30) ◽  
pp. 1450184 ◽  
Author(s):  
Alexander Reshetnyak
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Landau Gauge ◽  
Functional Integral ◽  
Yang Mills ◽  
Gauge Models ◽  
S Matrix ◽  
Gauge Fixing ◽  
Dependent Parameter ◽  
Quantum Treatment

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

scholarly journals The Quantum Description of BF Model in Superspace

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Manoj Kumar Dwivedi
Keyword(s):  
Brst Symmetry ◽  
Landau Gauge ◽  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Topological Theory ◽  
Quantum Description ◽  
Bf Theory ◽  
Standard Field ◽  
Shift Symmetry ◽  
Superspace Description

We consider the BRST symmetric four-dimensional BF theory, a topological theory, containing antisymmetric tensor fields in Landau gauge and extend the BRST symmetry by introducing a shift symmetry to it. Within this formulation, the antighost fields corresponding to shift symmetry coincide with antifields of standard field/antifield formulation. Furthermore, we provide a superspace description for the BF model possessing extended BRST and extended anti-BRST transformations.

STOCHASTIC GAUGE-FIXING FOR NON-ABELIAN ANTISYMMETRIC TENSOR FIELDS

1991 ◽  
Vol 06 (36) ◽  
pp. 3331-3339
Author(s):  
ATSUSHI NAKAMURA
Keyword(s):  
Gauge Theories ◽  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Gauge Fixing ◽  
Brst Invariance

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.

TOPOLOGICAL YANG-MILLS THEORY WITH VECTOR AND ANTISYMMETRIC TENSOR FIELDS

1995 ◽  
Vol 10 (25) ◽  
pp. 3649-3662 ◽  
Author(s):  
DAE SUNG HWANG
Keyword(s):  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Brst Transformation ◽  
Classical Action ◽  
Yang Mills ◽  
Transformation Rules ◽  
The Matrix ◽  
Extended Field ◽  
Quantum Action ◽  
Matrix Derivative

We study a system composed of vector and second rank antisymmetric tensor gauge fields in the superconnection framework. We incorporate the matrix derivative of non-commutative geometry in order to induce the topological Yang-Mills theory. In this structure we get the BRST and anti-BRST transformation rules from one horizontality condition, and obtain the topological classical action naturally from the extended field strength. We obtain its quantum action through the BRST formalism.

GAUGE FIXING FOR LINEARIZED GRAVITY AND ANTISYMMETRIC TENSOR FIELDS

1990 ◽  
Vol 05 (11) ◽  
pp. 2145-2154
Author(s):  
DEBASHIS GANGOPADHYAY
Keyword(s):  
Tensor Field ◽  
Antisymmetric Tensor ◽  
Projection Operators ◽  
Tensor Fields ◽  
Linearized Gravity ◽  
Longitudinal Modes ◽  
Covariant Derivatives ◽  
Antisymmetric Tensor Field ◽  
Gauge Fixing

Using the functional stochastic scheme, the gauge fixing term for linearized gravity is shown to be related to longitudinal modes within the framework of the usual set of momentum projection operators. A similar analysis is done for non-Abelian antisymmetric tensor field by replacing derivatives with covariant derivatives in all relevant equations and by constructing suitable operators for projecting out transverse and longitudinal modes.

scholarly journals Generalization of Faddeev–Popov rules in Yang–Mills theories: N = 3,4 BRST symmetries

2018 ◽  
Vol 33 (03) ◽  
pp. 1850006 ◽  
Author(s):  
Alexander Reshetnyak
Keyword(s):  
Irreducible Representation ◽  
Classical Model ◽  
Brst Symmetry ◽  
Classical Action ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Change Of Variables ◽  
Gauge Fixing ◽  
Quantum Action

The Faddeev–Popov rules for a local and Poincaré-covariant Lagrangian quantization of a gauge theory with gauge group are generalized to the case of an invariance of the respective quantum actions, [Formula: see text], with respect to [Formula: see text]-parametric Abelian SUSY transformations with odd-valued parameters [Formula: see text], [Formula: see text] and generators [Formula: see text]: [Formula: see text], for [Formula: see text], implying the substitution of an [Formula: see text]-plet of ghost fields, [Formula: see text], instead of the parameter, [Formula: see text], of infinitesimal gauge transformations: [Formula: see text]. The total configuration spaces of fields for a quantum theory of the same classical model coincide in the [Formula: see text] and [Formula: see text] symmetric cases. The superspace of [Formula: see text] SUSY irreducible representation includes, in addition to Yang–Mills fields [Formula: see text], [Formula: see text] ghost odd-valued fields [Formula: see text], [Formula: see text] and [Formula: see text] even-valued [Formula: see text] for [Formula: see text], [Formula: see text]. To construct the quantum action, [Formula: see text], by adding to the classical action, [Formula: see text], of an [Formula: see text]-exact gauge-fixing term (with gauge fermion), a gauge-fixing procedure requires [Formula: see text] additional fields, [Formula: see text]: antighost [Formula: see text], [Formula: see text] even-valued [Formula: see text], 3 odd-valued [Formula: see text] and Nakanishi–Lautrup [Formula: see text] fields. The action of [Formula: see text] transformations on new fields as [Formula: see text]-irreducible representation space is realized. These transformations are the [Formula: see text] BRST symmetry transformations for the vacuum functional, [Formula: see text]. The space of all fields [Formula: see text] proves to be the space of an irreducible representation of the fields [Formula: see text] for [Formula: see text]-parametric SUSY transformations, which contains, in addition to [Formula: see text] the [Formula: see text] ghost–antighost, [Formula: see text], even-valued, [Formula: see text], odd-valued [Formula: see text] and [Formula: see text] fields. The quantum action is constructed by adding to [Formula: see text] an [Formula: see text]-exact gauge-fixing term with a gauge boson, [Formula: see text]. The [Formula: see text] SUSY transformations are by [Formula: see text] BRST transformations for the vacuum functional, [Formula: see text]. The procedures are valid for any admissible gauge. The equivalence with [Formula: see text] BRST-invariant quantization method is explicitly found. The finite [Formula: see text] BRST transformations are derived and the Jacobians for a change of variables related to them but with field-dependent parameters in the respective path integral are calculated. They imply the presence of a corresponding modified Ward identity related to a new form of the standard Ward identities and describe the problem of a gauge-dependence. An introduction into diagrammatic Feynman techniques for [Formula: see text] BRST invariant quantum actions for Yang–Mills theory is suggested.

scholarly journals ON p – q DUALITY AND EXPLICIT SOLUTIONS IN c ≤ 1 2D GRAVITY MODELS

1995 ◽  
Vol 10 (08) ◽  
pp. 1219-1236 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
2D Gravity ◽  
Integral Formula ◽  
Integral Representations ◽  
Gravity Models ◽  
Explicit Solutions ◽  
String Equation ◽  
Duality Transformation

We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.

Massive totally antisymmetric tensor fields, a systematic study

1987 ◽  
Vol 97 (2) ◽  
pp. 141-169
Author(s):  
A. Z. Capri ◽  
M. Kobatashi
Keyword(s):  
Systematic Study ◽  
Antisymmetric Tensor ◽  
Tensor Fields

scholarly journals Antisymmetric tensor fields in Randall–Sundrum thick branes

2010 ◽  
Vol 693 (4) ◽  
pp. 503-508 ◽  
Author(s):  
G. Alencar ◽  
R.R. Landim ◽  
M.O. Tahim ◽  
C.R. Muniz ◽  
R.N. Costa Filho
Keyword(s):  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Thick Branes

scholarly journals BRST Quantization of the Proca Model Based on the BFT and the BFV Formalism

1997 ◽  
Vol 12 (23) ◽  
pp. 4217-4239 ◽  
Author(s):  
Yong-Wan Kim ◽  
Mu-In Park ◽  
Young-Jai Park ◽  
Sean J. Yoon
Keyword(s):  
Phase Space ◽  
Brst Quantization ◽  
Brst Symmetry ◽  
Mass Term ◽  
Class Constraint ◽  
Extended Phase ◽  
Breaking Effect ◽  
Linear Character ◽  
Constraint System ◽  
Gauge Fixing

The BRST quantization of the Abelian Proca model is performed using the Batalin–Fradkin–Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev–Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the Stückelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.

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