scholarly journals Physical quantities and arbitrariness in resolving quantum master equation

2017 ◽  
Vol 32 (11) ◽  
pp. 1750068 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov
Keyword(s):  
Master Equation ◽  
Path Integral ◽  
Quantum Master Equation ◽  
Abelian Gauge ◽  
Quantization Procedure ◽  
Gauge Fixing ◽  
Physical Quantities

By proceeding with the idea that the presence of physical (BRST invariant) extra factors in the path integral is equivalent to taking into account explicitly the arbitrariness in resolving the quantum master equation, we consider the field–antifield quantization procedure both with the Abelian and the non-Abelian gauge fixing.

scholarly journals Can quantum fluctuations differentiate between standard and unimodular gravity?

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Gustavo P. de Brito ◽  
Oleg Melichev ◽  
Roberto Percacci ◽  
Antonio D. Pereira
Keyword(s):  
Scalar Field ◽  
Path Integral ◽  
Invariant Theory ◽  
Quantum Fluctuations ◽  
Quantization Procedure ◽  
Gauge Fixing ◽  
Theory Of Gravity ◽  
Definition Of

Abstract We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones.

scholarly journals EMERGENCE OF THE HAAR MEASURE IN THE STANDARD FUNCTIONAL INTEGRAL REPRESENTATION OF THE YANG-MILLS PARTITION FUNCTION

1996 ◽  
Vol 11 (30) ◽  
pp. 2451-2461 ◽  
Author(s):  
H. REINHARDT
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Haar Measure ◽  
Transition Amplitude ◽  
Functional Integral ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Gauge Fixing ◽  
Popov Method

The conventional path integral expression for the Yang–Mills transition amplitude with flat measure and gauge-fixing built in via the Faddeev-Popov method has been claimed to fall short of guaranteeing gauge invariance in the nonperturbative regime. We show, however, that it yields the gauge-invariant partition function where the projection onto gauge-invariant wave functions is explicitly performed by integrating over the compact gauge group. In a variant of maximal Abelian gauge the Haar measure arises in the conventional Yang-Mills path integral from the Faddeev-Popov determinant.

scholarly journals Quantum localization of classical mechanics

2016 ◽  
Vol 31 (22) ◽  
pp. 1650128
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov
Keyword(s):  
Partition Function ◽  
Master Equation ◽  
Path Integral ◽  
Classical Mechanics ◽  
Special Solution ◽  
Unitary Limit ◽  
Special Choice ◽  
Classical Action ◽  
Gauge Fixing ◽  
Quantum Localization

Quantum localization of classical mechanics within the BRST-BFV and BV (or field–antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.

A study of the path-integral quantization of Abelian gauge theories when no explicit gauge-fixing term is included in the bilinear part of the gauge-field action

1985 ◽  
Vol 63 (10) ◽  
pp. 1334-1336
Author(s):  
Stephen Phillips
Keyword(s):  
Gauge Field ◽  
Path Integral ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Abelian Gauge ◽  
Gaussian Form ◽  
Path Integral Quantization ◽  
Field Action ◽  
Gauge Fixing

The mathematical problem of inverting the operator [Formula: see text] as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article.Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, [Formula: see text], can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one.Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action.

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.

LIGHT-FRONT HAMILTONIAN AND PATH INTEGRAL QUANTIZATION OF VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM

2012 ◽  
Vol 27 (27) ◽  
pp. 1250157 ◽  
Author(s):  
USHA KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Light Cone ◽  
Mass Term ◽  
Light Front ◽  
Light Cone Gauge ◽  
Schwinger Model ◽  
Path Integral Quantization ◽  
New Class ◽  
Gauge Fixing ◽  
Form Theory

Vector Schwinger model with a mass term for the photon, describing 2D electrodynamics with massless fermions, studied by us recently [U. Kulshreshtha, Mod. Phys. Lett. A22, 2993 (2007); U. Kulshreshtha and D. S. Kulshreshtha, Int. J. Mod. Phys. A22, 6183 (2007); U. Kulshreshtha, PoS LC2008, 008 (2008)], represents a new class of models. This theory becomes gauge-invariant when studied on the light-front. This is in contrast to the instant-form theory which is gauge-non-invariant. In this work, we study the light-front Hamiltonian and path integral quantization of this theory under appropriate light-cone gauge-fixing. The discretized light-cone quantization of the theory where we wish to make contact with the experimentally observational aspects of the theory would be presented in a separate paper.

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