scholarly journals Finite BRST–BFV transformations for dynamical systems with second-class constraints

2015 ◽  
Vol 30 (21) ◽  
pp. 1550108 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov ◽  
Igor V. Tyutin
Keyword(s):  
Dynamical Systems ◽  
Finite Field ◽  
Path Integral ◽  
Hamiltonian Formalism ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Compensation Equation

We study finite field-dependent BRST–BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, 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 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–anti-BRST 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–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST 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 λaand 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 Rξ-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 S-matrix in the Lagrangian approach.

scholarly journals A systematic study of finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism

2014 ◽  
Vol 29 (23) ◽  
pp. 1450128 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov ◽  
Igor V. Tyutin
Keyword(s):  
Field Dependence ◽  
Path Integral ◽  
Systematic Study ◽  
Hamiltonian Formalism ◽  
Gauge Fixing ◽  
Compensation Equation

We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

scholarly journals A systematic study of finite field-dependent BRST-BV transformations in Sp(2) extended field–antifield formalism

2014 ◽  
Vol 29 (29) ◽  
pp. 1450167 ◽  
Author(s):  
Igor A. Batalin ◽  
Klaus Bering ◽  
Peter M. Lavrov ◽  
Igor V. Tyutin
Keyword(s):  
Finite Field ◽  
Path Integral ◽  
Systematic Study ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Extended Field

In the framework of Sp(2) extended Lagrangian field–antifield BV formalism, we study systematically the role of finite field-dependent BRST-BV transformations. We have proved that the Jacobian of a finite BRST-BV transformation is capable of generating arbitrary finite change of the gauge-fixing function in the path integral.

scholarly journals A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (23) ◽  
pp. 1450127 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov ◽  
Igor V. Tyutin
Keyword(s):  
Field Dependence ◽  
Path Integral ◽  
Systematic Study ◽  
Hamiltonian Formalism ◽  
Gauge Fixing ◽  
Compensation Equation

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

APPLICATION OF FINITE FIELD-DEPENDENT BRS TRANSFORMATIONS TO PROBLEMS OF THE COULOMB GAUGE

2002 ◽  
Vol 17 (09) ◽  
pp. 1279-1299 ◽  
Author(s):  
SATISH D. JOGLEKAR ◽  
BHABANI PRASAD MANDAL
Keyword(s):  
Finite Field ◽  
Path Integral ◽  
Ad Hoc ◽  
High Energy ◽  
Coulomb Gauge ◽  
Gauge Parameter ◽  
Path Integral Formulation ◽  
High Energy Behavior ◽  
Energy Behavior ◽  
Field Dependent

We discuss the Coulomb propagator in the formalism developed recently in which we construct the Coulomb gauge path-integral by correlating it with the well-defined Lorentz gauge path-integrals through a finite field-dependent BRS transformation. We discover several features of the Coulomb gauge from it. We find that the singular Coulomb gauge has to be treated as the gauge parameter λ → 0 limit. We further find that the propagator so obtained has good high energy behavior[Formula: see text] for λ ≠ 0 and ∊ ≠ 0. We also find that the behavior of the propagator so obtained is sensitive to the order of limits k0→ ∞, λ → 0 and ∊ → 0; so that these have to be handled carefully in a higher loop calculation. We show that we can arrive at the result of Cheng and Tsai for the ambiguous two-loop Feynman integrals without the need for an extra ad hoc regularization and within the path integral formulation.

scholarly journals CORRECT TREATMENT OF $\bm{{1\over (\eta\cdot{\lc{k}})^{\lc{p}}}}$ SINGULARITIES IN THE AXIAL GAUGE PROPAGATOR

2000 ◽  
Vol 15 (10) ◽  
pp. 1453-1479 ◽  
Author(s):  
SATISH D. JOGLEKAR ◽  
A. MISRA
Keyword(s):  
Finite Field ◽  
Path Integral ◽  
Small Region ◽  
Alternative Procedure ◽  
Complicated Structure ◽  
Integral Formalism ◽  
Correct Treatment ◽  
Text Type ◽  
Axial Gauge ◽  
Field Dependent

The propagators in axial-type, light-cone and planar gauges contain [Formula: see text]-type singularities. These singularities have generally been treated by inventing prescriptions for them. In this work, we propose an alternative procedure for treating these singularities in the path integral formalism using the known way of treating the singularities in Lorentz gauges. To this end, we use a finite field-dependent BRS transformation that interpolates between Lorentz-type and the axial-type gauges. We arrive at the ε-dependent tree propagator in the axial-type gauges. We examine the singularity structure of the propagator and find that the axial gauge propagator so constructed has no spurious poles (for real k). It however has a complicated structure in a small region near η·k=0. We show how this complicated structure can effectively be replaced by a much simpler propagator.

scholarly journals On the BRST and finite field-dependent BRST of a model where vector and axial vector interactions get mixed up with different weights

2016 ◽  
Vol 31 (32) ◽  
pp. 1650171 ◽  
Author(s):  
Safia Yasmin ◽  
Anisur Rahaman
Keyword(s):  
Gauge Symmetry ◽  
Finite Field ◽  
Axial Vector ◽  
Dimensional Model ◽  
Brst Transformation ◽  
Gauge Invariant ◽  
Local Gauge Symmetry ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Lower Dimensional

The generalized version of a lower dimensional model where vector and axial vector interactions get mixed up with different weights is considered. The bosonized version of which does not possess the local gauge symmetry. An attempt has been made here to construct the BRST invariant reformulation of this model using Batalin–Fradlin and Vilkovisky formalism. It is found that the extra field needed to make it gauge invariant turns into Wess–Zumino scalar with appropriate choice of gauge fixing. An application of finite field-dependent BRST and anti-BRST transformation is also made here in order to show the transmutation between the BRST symmetric and the usual nonsymmetric version of the model.

scholarly journals A systematic study of finite BRST-BV transformations in field–antifield formalism

2014 ◽  
Vol 29 (29) ◽  
pp. 1450166 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov ◽  
Igor V. Tyutin
Keyword(s):  
Field Dependence ◽  
Path Integral ◽  
Systematic Study ◽  
Gauge Fixing ◽  
Compensation Equation

We study systematically finite BRST-BV transformations in the field–antifield formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

Beta dynamical systems over the formal fields

2014 ◽  
Vol 51 (4) ◽  
pp. 454-465
Author(s):  
Lu-Ming Shen ◽  
Huiping Jing
Keyword(s):  
Dynamical Systems ◽  
Finite Field ◽  
Haar Measure ◽  
Laurent Series ◽  
Formal Laurent Series ◽  
Almost All

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q ((X^{ - 1} ))$$ \end{document} denote the formal field of all formal Laurent series x = Σ n=ν∞anX−n in an indeterminate X, with coefficients an lying in a given finite field \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}. For any \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} with deg β > 1, it is known that for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} (with respect to the Haar measure), x is β-normal. In this paper, we show the inverse direction, i.e., for any x, for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document}, x is β-normal.

GENERAL COVARIANCE, TOPOLOGICAL QUANTUM FIELD THEORIES AND FRACTIONAL STATISTICS

1992 ◽  
Vol 07 (02) ◽  
pp. 209-234 ◽  
Author(s):  
J. GAMBOA
Keyword(s):  
Hamiltonian Formalism ◽  
Field Theories ◽  
General Covariance ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Fractional Statistics ◽  
Multiply Connected ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Topological Quantum Field Theories

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. We study the relationship between both theories in 2 + 1 dimensions and we show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST–BFV quantization is reviewed in order to understand the topological approach proposed here.

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