19 research outputs found
Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories
We introduce the notion of finite BRST-antiBRST transformations, both global
and field-dependent, with a doublet , , of anticommuting
Grassmann parameters and find explicit Jacobians corresponding to these changes
of variables in Yang-Mills theories. It turns out that the finite
transformations are quadratic in their parameters. At the same time, exactly as
in the case of finite field-dependent BRST transformations for the Yang-Mills
vacuum functional, special field-dependent BRST-antiBRST transformations, with
-potential parameters induced by a finite
even-valued functional and by the anticommuting generators of
BRST-antiBRST transformations, amount to a precise change of the gauge-fixing
functional. This proves the independence of the vacuum functional under such
BRST-antiBRST transformations. We present the form of transformation parameters
that generates a change of the gauge in the path integral and evaluate it
explicitly for connecting two arbitrary -like gauges. For arbitrary
differentiable gauges, the finite field-dependent BRST-antiBRST transformations
are used to generalize the Gribov horizon functional , given in the Landau
gauge, and being an additive extension of the Yang-Mills action by the Gribov
horizon functional in the Gribov-Zwanziger model. This generalization is
achieved in a manner consistent with the study of gauge independence. We also
discuss an extension of finite BRST-antiBRST\ transformations to the case of
general gauge theories and present an ansatz for such transformations.Comment: 31 pages, no figures, misprint in the Eq. (5.1) correcte
Finite BRST-antiBRST Transformations in Generalized Hamiltonian Formalism
We introduce the notion of finite BRST-antiBRST transformations for
constrained dynamical systems in the generalized Hamiltonian formalism, both
global and field-dependent, with a doublet , , of
anticommuting Grassmann parameters and find explicit Jacobians corresponding to
these changes of variables in the path integral. It turns out that the finite
transformations are quadratic in their parameters. Exactly as in the case of
finite field-dependent BRST-antiBRST transformations for the Yang--Mills vacuum
functional in the Lagrangian formalism examined in our previous paper
[arXiv:1405.0790[hep-th]], special field-dependent BRST-antiBRST
transformations with functionally-dependent parameters \lambda_{a}=\int
dt\(s_{a}\Lambda) , generated by a finite even-valued function
and by the anticommuting generators of BRST-antiBRST transformations,
amount to a precise change of the gauge-fixing function for arbitrary
constrained dynamical systems. This proves the independence of the vacuum
functional under such transformations. We derive a new form of the Ward
identities, depending on the parameters , and study the problem of
gauge-dependence. We present the form of transformation parameters which
generates a change of the gauge in the Hamiltonian path integral, evaluate it
explicitly for connecting two arbitrary -like gauges in the
Yang--Mills theory and establish, after integration over momenta, a coincidence
with the Lagrangian path integral [arXiv:1405.0790[hep-th]], which justifies
the unitarity of the -matrix in the Lagrangian approach.Comment: 23 pages, published version, no figures, 1 table, presentation
improved, references [17], [27] updated, ref. [40] and comments added. arXiv
admin note: text overlap with arXiv:1405.079
Field-Dependent BRST-antiBRST Lagrangian Transformations
We continue our study of finite BRST-antiBRST transformations for general
gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790[hep-th]
and arXiv:1406.0179[hep-th]], with a doublet , , of
anticommuting Grassmann parameters and prove the correctness of the explicit
Jacobian in the partition function announced in [arXiv:1406.0179[hep-th]],
which corresponds to a change of variables with functionally-dependent
parameters induced by a finite Bosonic functional
and by the anticommuting generators of
BRST-antiBRST transformations in the space of fields and auxiliary
variables . We obtain a Ward identity depending on the
field-dependent parameters and study the problem of gauge
dependence, including the case of Yang--Mills theories. We examine a
formulation with BRST-antiBRST symmetry breaking terms, additively introduced
to the quantum action constructed by the Sp(2)-covariant Lagrangian rules,
obtain the Ward identity and investigate the gauge-independence of the
corresponding generating functional of Green's functions. A formulation with
BRST symmetry breaking terms is developed. It is argued that the gauge
independence of the above generating functionals is fulfilled in the BRST and
BRST-antiBRST settings. These concepts are applied to the average effective
action in Yang--Mills theories within the functional renormalization group
approach.Comment: 20+7 pages, no figures, presentation improved, typos corrected,
reference added, remarks on composite field approach added in Sec. 4 and App.
Finite BRST-antiBRST Transformations in Lagrangian Formalism
We continue the study of finite BRST-antiBRST transformations for general
gauge theories in Lagrangian formalism initiated in [arXiv:1405.0790[hep-th]],
with a doublet , , of anticommuting Grassmann parameters,
and find an explicit Jacobian corresponding to this change of variables for
constant . This makes it possible to derive the Ward identities
and their consequences for the generating functional of Green's functions. We
announce the form of the Jacobian [proved to be correct in
[arXiv:1406.5086[hep-th]] for finite field-dependent BRST-antiBRST
transformations with functionally-dependent parameters, , induced by a finite even-valued functional and by the generators of BRST-antiBRST transformations
acting in the space of fields , antifields , and auxiliary variables . On the basis of this
Jacobian, we solve a compensation equation for , which is used to
achieve a precise change of the gauge-fixing functional for an arbitrary gauge
theory. We derive a new form of the Ward identities containing the parameters
and study the problem of gauge-dependence. The general approach
is exemplified by the Freedman--Townsend model of\ a non-Abelian antisymmetric
tensor field.Comment: 11 pages, no figures, (5.9) and Discussion extended, section with
Freedman-Townsend model, 4+6 references and acknowledgments adde
Finite BRST Mapping in Higher Derivative Models
We continue the study of finite field dependent BRST (FFBRST) symmetry in the
quantum theory of gauge fields. An expression for the Jacobian of path integral
measure is presented, depending on a finite field-dependent parameter, and the
FFBRST symmetry is then applied to a number of well-established quantum gauge
theories in a form which includes higher-derivative terms. Specifically, we
examine the corresponding versions of the Maxwell theory, non-Abelian vector
field theory, and gravitation theory. We present a systematic mapping between
different forms of gauge-fixing, including those with higher-derivative terms,
for which these theories have better renormalization properties. In doing so,
we also provide the independence of the S-matrix from a particular gauge-fixing
with higher derivatives. Following this method, a higher-derivative quantum
action can be constructed for any gauge theory in the FFBRST framework.Comment: 9 pages, published in Braz. J. Phy
On gauge fixing in the Lagrangian formalism of superfield BRST quantization
We propose a modification of the gauge-fixing procedure in the Lagrangian
method of superfield BRST quantization for general gauge theories which
simultaneously provides a natural generalization of the well-known BV
quantization scheme as far as gauge-fixing is concerned. A superfield form of
BRST symmetry for the vacuum functional is found. The gauge-independence of the
S-matrix is established.Comment: 8 pages, LATEX Includes additional Reference and relation to i
BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields
We construct a Lagrangian description of irreducible half-integer higher-spin
representations of the Poincare group with the corresponding Young tableaux
having two rows, on a basis of the BRST approach. Starting with a description
of fermionic higher-spin fields in a flat space of any dimension in terms of an
auxiliary Fock space, we realize a conversion of the initial operator
constraint system (constructed with respect to the relations extracting
irreducible Poincare-group representations) into a first-class constraint
system. For this purpose, we find auxiliary representations of the constraint
subsuperalgebra containing the subsystem of second-class constraints in terms
of Verma modules. We propose a universal procedure of constructing
gauge-invariant Lagrangians with reducible gauge symmetries describing the
dynamics of both massless and massive fermionic fields of any spin. No
off-shell constraints for the fields and gauge parameters are used from the
very beginning. It is shown that the space of BRST cohomologies with a
vanishing ghost number is determined only by the constraints corresponding to
an irreducible Poincare-group representation. To illustrate the general
construction, we obtain a Lagrangian description of fermionic fields with
generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the
complete set of auxiliary fields and gauge symmetries.Comment: 41 pages, no figures, corrected typos, updated introduction, sections
5, 7.1, 7.2 with examples, conclusion with all basic results unchanged,
corrected formulae (3.27), (7.138), (7.140), added dimensional reduction part
with formulae (5.34)-(5.48), (7.8)-(7.10), (7.131)-(7.136), (7.143)-(7.164),
added Refs. 52, 53, 54, examples for massive fields developed by 2 way
Field-dependent BRST–antiBRST transformations in Yang–Mills and Gribov–Zwanziger theories
AbstractWe introduce the notion of finite BRST–antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang–Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang–Mills vacuum functional, special field-dependent BRST–antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa of BRST–antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST–antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST–antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang–Mills action by the Gribov horizon functional in the Gribov–Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST–antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations