Related papers: Complete Computation of DeWitt-Seeley-Gilkey Coeff…
Computer algebra methods are applied to investigation of spectral asymptotics of elliptic differential operators on curved manifolds with torsion and in the presence of a gauge field. In this paper we present complete expressions for the…
The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the…
De Witt--Seeley--Gilkey coefficients are calculated for the most general minimal differential fourth--order operator on Riemannian space of an arbitrary dimension.
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…
The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…
We suggest a systematic calculational scheme for heat kernels of covariant nonminimal operators in causal theories whose characteristic surfaces are null with respect to a generic metric. The calculational formalism is based on a…
A method for calculation of the DWSG coefficients for operators in spaces with metric incompatible with connection is suggested based on a generalization of the pseudodifferential operators technique. By using the proposed method, the…
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…
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…
We consider certain results for the heat kernel of nonminimal operators. The general expressions provided by Gusynin and Kornyak resulting from symbolic computation programmes for n dimensions are evaluated for 4 dimensions which are…
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…
We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…
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…
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…
For a given bounded domain $\Omega$ with smooth boundary in a smooth Riemannian manifold $(\mathcal{M},g)$, we establish a procedure to get all the coefficients of the asymptotic expansion of the trace of the heat kernel associated with the…
We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking…
In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The Seeley-DeWitt coefficients of this decomposition…
We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain…
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…