Related papers: Heat kernel expansion: user's manual

We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity is of order two…

We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study…

In this paper we establish the existence and uniqueness of heat kernels to a large class of time-inhomogenous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates,…

We introduce a new method that exploits the combination of the Heat Kernel (HK) and Background Field Method to compute gauge-invariant and gauge parameter-independent quantities such as the effective potential, anomalous dimensions, and…

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…

In this paper some techniques useful to perform quantum field theory computations in a covariant manner are reviewed. In particular the background field gauge, the zeta function regularization and the heat kernel approach are highlighted.…

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…

We consider skew extensions of expanding maps by compact Lie groups. For a class of natural invariant measures, we prove an explicit lower bound on the rate of (exponential) mixing involving topological pressure. Proof uses representation…

In this paper, we generally expressed the virial expansion of ideal quantum gases by the heat kernel coefficients for the corresponding Laplace type operator. As examples, we give the virial coefficients for quantum gases in $d$-dimensional…

This paper is an exposition of several questions linking heat kernel measures on infinite dimensional Lie groups, limits associated with critical Sobolev exponents, and Feynmann-Kac measures for sigma models.

In this paper, we demonstrate that not only the heat kernel techniques are useful for computation of the parity anomaly, but also the parity anomaly turns out to be a powerful mean in studying the heat kernel. We show that the gravitational…

Perturbation theory is an important tool to describe the properties of QCD at very high temperatures. Recently a new technique has been proposed to compute the one-loop effective action of QCD at finite temperature by making a gauge…

We present an overview of recent nonperturbative results in the theory of heat kernel and its late time asymptotics responsible for the infrared behavior of quantum effective action for massless theories. In particular, we derive the…

The one--loop effective action for the case of a massive scalar loop in the background of both a scalar potential and an abelian or non--abelian gauge field is written in a one--dimensional path integral representation. From this the…

Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…

In this paper, we focus on strongly local regular Dirichlet forms, especially those satisfying Morrey-type inequalities. We prove the equivalence between resistance estimates and heat kernel estimates in this case. Self-similar forms on…

It is well known that short-time expansions of heat kernels correlate to formal high-frequency expansions of spectral densities. It is also well known that the latter expansions are generally not literally true beyond the first term.…

We generalize the Endo formula originally developed for the computation of the heat kernel asymptotic expansion for non-minimal operators in commutative gauge theories to the noncommutative case. In this way, the first three non-zero heat…

We obtain matching two sided estimates of the heat kernel on a connected sum of parabolic manifolds, each of them satisfying the Li-Yau estimate. The key result is the on-diagonal upper bound of the heat kernel at a central point. Contrary…

I give a short guide into applications of the heat kernel technique to string/brane physics with an emphasis on the emerging boundary value problems.