English
Related papers

Related papers: Heat kernel expansion for higher order minimal and…

200 papers

We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…

Mathematical Physics · Physics 2011-02-17 Ivan G. Avramidi , Guglielmo Fucci

A method is suggested for the calculation of the DeWitt-Seeley-Gilkey (DWSG) coefficients for the operator $\sqrt{-\nabla^2 + V(x)}$ basing on a generalization of the pseudodifferential operator technique. The lowest DWSG coefficients for…

High Energy Physics - Theory · Physics 2009-10-30 E. V. Gorbar

An overview about recent progress in the calculation of the heat kernel and the one-loop effective action in quantum gravity and gauge theories is given. We analyse the general structure of the standard Schwinger-De Witt asymptotic…

General Relativity and Quantum Cosmology · Physics 2007-05-23 I. G. Avramidi

The heat kernel expansion for field theory at finite temperature is constructed. It is based on the imaginary time formalism and applies to generic Klein-Gordon operators in flat space-time. Full gauge invariance is manifest at each order…

High Energy Physics - Phenomenology · Physics 2008-11-26 E. Megias , E. Ruiz Arriola , L. L. Salcedo

We review the status of covariant methods in quantum field theory and quantum gravity, in particular, some recent progress in the calculation of the effective action via the heat kernel method. We study the heat kernel associated with an…

High Energy Physics - Theory · Physics 2014-06-06 Ivan G. Avramidi

The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential…

Differential Geometry · Mathematics 2020-02-07 Shantanu Dave , Stefan Haller

We consider expansions for the kernels of operator functions of second-order minimal operators on a curved background. We show that the terms of these expansions originate in the ultraviolet or infrared regions. We propose a systematic…

High Energy Physics - Theory · Physics 2026-03-26 A. O. Barvinsky , A. E. Kalugin , W. Wachowski

The generator of time-translations on the solution space of the wave equation on stationary spacetimes specialises to the square root of the Laplacian on Riemannian manifolds when the spacetime is ultrastatic. Its spectral analysis…

Spectral Theory · Mathematics 2026-04-06 Alexander Strohmaier , Steve Zelditch

The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family $\H(r;g)$ of…

Differential Geometry · Mathematics 2022-03-28 Andreas Juhl

The heat kernel in curved space-time is computed to fourth order in a strict expansion in the number of covariant derivatives. The computation is made for arbitrary non abelian gauge and scalar fields and for the Riemann connection in the…

High Energy Physics - Theory · Physics 2008-11-26 L. L. Salcedo

We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…

Mathematical Physics · Physics 2009-11-07 Ivan Avramidi

Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In…

Statistical Mechanics · Physics 2016-09-06 Yu-Zi Gou , Wen-Du Li , Ping Zhang , Wu-Sheng Dai

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the…

Differential Geometry · Mathematics 2022-01-19 Matthias Ludewig

The method of covariant symbols of Pletnev and Banin is extended to space-times with topology $\R^n\times S^1\times ... \times S^1$. By means of this tool, we obtain explicit formulas for the diagonal matrix elements and the trace of the…

High Energy Physics - Theory · Physics 2012-02-15 F. J. Moral-Gamez , L. L. Salcedo

The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…

High Energy Physics - Theory · Physics 2008-11-26 D. V. Vassilevich

Asymptotic heat kernel expansion for nonminimal differential operators on curved manifolds in the presence of gauge fields is considered. The complete expressions for the fourth coefficient E_4 in the heat kernel expansion for such…

Numerical Analysis · Mathematics 2025-10-20 Valery P. Gusynin , Vladimir V. Kornyak

We present a diagram technique used to calculate the Seeley-DeWitt coefficients for a covariant Laplace operator. We use the combinatorial properties of the coefficients to construct a matrix formalism and derive a formula for an arbitrary…

High Energy Physics - Theory · Physics 2019-05-15 A. V. Ivanov

In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…

Mathematical Physics · Physics 2014-05-15 Guglielmo Fucci

We consider the heat equation associated with a class of second order hypoelliptic H\"{o}rmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a…

Analysis of PDEs · Mathematics 2015-10-19 Davide Barilari , Elisa Paoli

By applying the covariant Taylor expansion method, the fifth lower coefficients the asymptotic expansion of the heat kernel associated with a fermion of spin 1/2 in Riemann-Cartan space are manifestly given. These coefficients in…

High Energy Physics - Theory · Physics 2007-05-23 S. Yajima , Y. Higasida , K. Kawano , S. -I. Kubota