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.

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 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 The two-sphere partition function in two-dimensional quantum gravity

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Dionysios Anninos ◽  
Teresa Bautista ◽  
Beatrix Mühlmann
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Central Charge ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Positive Cosmological Constant ◽  
Gauge Fixing ◽  
Semiclassical Expansion

Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman 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.

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.

scholarly journals BRST Formulation of Partition Function Constraints

1997 ◽  
Vol 12 (15) ◽  
pp. 1119-1126 ◽  
Author(s):  
Jorge Alfaro ◽  
Klaus Bering ◽  
Poul H. Damgaard
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Master Equation ◽  
High Order ◽  
Generating Functional ◽  
Nilpotent Operators ◽  
External Sources

We show that the constraints on the generating functional have direct BRST-extensions in terms of nilpotent operators Δ that annihilate this generating functional, and which may be of arbitrarily high order. The free energy F in the presence of external sources thus satisfies a "Master Equation" which is described in terms of a tower of higher antibrackets.

A non-perturbative path-integral based thermal cluster expansion approach for grand partition function of quantum systems

2002 ◽  
Vol 352 (1-2) ◽  
pp. 63-69 ◽  
Author(s):  
Sheikh Hannan Mandal ◽  
Rathindranath Ghosh ◽  
Goutam Sanyal ◽  
Debashis Mukherjee
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Cluster Expansion ◽  
Quantum Systems ◽  
Grand Partition Function

scholarly journals Vacuum energy of a nonrelativistic string with nontrivial boundary condition

2018 ◽  
Vol 33 (16) ◽  
pp. 1850097 ◽  
Author(s):  
A. Jahan ◽  
S. Sukhasena
Keyword(s):  
Boundary Condition ◽  
Partition Function ◽  
Classical Solution ◽  
Path Integral ◽  
Integral Method ◽  
Vacuum Energy ◽  
Nonrelativistic Quantum ◽  
Relative Angle ◽  
Path Integral Method

We derive the partition function of a nonrelativistic quantum string whose ends are allowed to freely move along the two-angled straight solid rods. We first derive the classical solution of the model and then use it to derive the partition function utilizing the path integral method. We show that the vacuum energy is the sum of the Lüscher potential plus a term which depends on the relative angle between the rods.

scholarly journals Lorentz-violating gaugeon formalism for rank-2 tensor theory

2019 ◽  
Vol 34 (30) ◽  
pp. 1950245
Author(s):  
Sudhaker Upadhyay ◽  
Mushtaq B. Shah ◽  
Prince A. Ganai
Keyword(s):  
Tensor Field ◽  
Vector Fields ◽  
Fock Space ◽  
Antisymmetric Tensor ◽  
Type I ◽  
Classical Action ◽  
Tensor Theory ◽  
Antisymmetric Tensor Field ◽  
Gauge Fixing ◽  
Rank 2

We develop a BRST symmetric gaugeon formalism for the Abelian rank-2 antisymmetric tensor field in the Lorentz-breaking framework. The Lorentz-breaking is achieved here by considering a proper subgroup of Lorentz group together with translation. In this scenario, the gaugeon fields together with the standard fields of the Abelian rank-2 antisymmetric tensor theory get mass. In order to develop the gaugeon formulation for this theory in very special relativity (VSR), we first introduce a set of dipole vector fields as a quantum gauge freedom to the action. In order to quantize the dipole vector fields, the VSR-modified gauge-fixing and corresponding ghost action are constructed as the classical action is invariant under a VSR-modified gauge transformation. Further, we present a Type I gaugeon formalism for the Abelian rank-2 antisymmetric tensor field theory in VSR. The gauge structures of Fock space constructed with the help of BRST charges are also discussed.

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