相关论文: Generalized heat kernel coefficients

We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admits an asymptotic expansion at t=0 with coefficients that…

Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four…

The heat kernel expansion on even-dimensional hyperbolic spaces is asymptotic at both short and long times, with interestingly different Borel properties for these short and long time expansions. Resummations in terms of incomplete gamma…

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions…

We report the calculation of the fourth coefficient in an expansion of the heat kernel of a non-minimal, non-abelian kinetic operator in an arbitrary background gauge in arbitrary space-time dimension. The fourth coefficient is shown to…

The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic differential second order operator is generalized to manifolds with boundary. The first boundary coefficients of the asymptotic expansion which are…

Let M be a smooth closed (compact without boundary) Riemannian manifold of dimension n and P a q-dimensional smooth submanifold of M. U will denote the tubular neighborhood of P in M. Let E be a smooth vector bundle over M. Here we will…

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…

We build a systematic calculational method for the covariant expansion of the two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal differential operators of any order. This is the expansion in powers of dimensional…

In this article, we prove a general and rather flexible upper bound for the heat kernel of a weighted heat operator on a closed manifold evolving by an intrinsic geometric flow. The proof is based on logarithmic Sobolev inequalities and…

We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…

I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In continuum theory its asymptotic expansion for t -> +0 provides geometric quantities, and therefore may be used to extract effective geometric quantities for fuzzy…

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…

We consider the heat kernel for higher-derivative and nonlocal operators in $d$-dimensional Euclidean space-time and its asymptotic behavior. As a building block for operators of such type, we consider the heat kernel of the minimal…

We give an asymptotic expansion of the relative entropy between the heat kernel $q_Z(t,z,w)$ of a compact Riemannian manifold $Z$ and the normalized Riemannian volume for small values of $t$ and for a fixed element $z\in Z$. We prove that…

Being motivated by physical applications (as the phi^4 model) we calculate the heat kernel coefficients for generalised Laplacians on the Moyal plane containing both left and right multiplications. We found both star-local and star-nonlocal…

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…

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…

We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…

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…