Heat kernel: proper-time method, Fock-Schwinger gauge, path integral, and Wilson line

DOI10.1134/S0040577920110057zbMath1453.81048arXiv1906.04019MaRDI QIDQ2215185

A. V. Ivanov, N. V. Kharuk

Publication date: 11 December 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.04019

zbMATH Keywords

path integralLaplace operatorheat kernelWilson lineFock-Schwinger gaugeordered exponentialproper time methodSeeley-Dewitt coefficient

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Feynman diagrams (81T18) Quantum field theory on curved space or space-time backgrounds (81T20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Heat kernel (35K08)

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Cites Work

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• Operators, geometry and quanta. Methods of spectral geometry in quantum field theory
• The spectral geometry of a Riemannian manifold
• Zeta function regularization of path integrals in curved spacetime
• Path integral formulae for heat kernels and their derivatives
• Heat kernel expansion: user's manual
• Heat kernel asymptotics, path integrals and infinite-dimensional determinants
• Three-loop Yang-Mills \(\beta\)-function via the covariant background field method
• On the application of the matrix formalism for the heat kernel to number theory
• Diagram technique for the heat kernel of the covariant Laplace operator
• Index theorems and domain walls
• Curvature and the eigenvalues of the Laplacian
• Curvature and the eigenforms of the Laplace operator
• A DeWitt expansion of the heat kernel for manifolds with a boundary
• Asymptotic expansion of the heat kernel for generalized boundary conditions
• b ₈ 'Hamidew' coefficient for a scalar field
• The Resolvent Parametrix of the General Elliptic Linear Differential Operator: A Closed Form for the Intrinsic Symbol
• Heat kernel asymptotics for mixed boundary conditions
• New invariants in the 1-loop divergences on manifolds with boundary
• Heat-kernel coefficients for oblique boundary conditions
• Index-free heat kernel coefficients
• The a _3/2 heat kernel coefficient for oblique boundary conditions
• Heat kernel expansion for semitransparent boundaries
• Heat Kernel and Quantum Gravity
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Quantum Theory of Gravity. I. The Canonical Theory
• Quantum Theory of Gravity. II. The Manifestly Covariant Theory
• Singular Integrals and Boundary Value Problems
• The Resolvent of an Elliptic Boundary Problem
• The index of elliptic operators on compact manifolds
• The Theory of Positrons
• On Gauge Invariance and Vacuum Polarization
• New developments in the Casimir effect