Related papers: Multiple reflection expansion and heat kernel coef…
The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of…
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…
Heat kernel expansion coefficients are calculated for vacuum fluctuations with distributional background potentials and field strengths. Terms up to and including t^5/2 are presented.
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…
We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic…
We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and…
In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By…
We consider the heat-kernel expansion of the massive Laplace operator on the three dimensional ball with Dirichlet boundary conditions. Using this example, we illustrate a very effective scheme for the calculation of an (in principle)…
We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and…
We study reflected jump diffusions on Ahlfors regular domains in general metric measure spaces. Under the condition that the Dirichlet form on the ambient space satisfies a capacity upper bound estimate, we construct an extension operator…
The first heat kernel coefficients are calculated for a dispersive ball whose permittivity at high frequency differs from unity by inverse powers of the frequency. The corresponding divergent part of the vacuum energy of the electromagnetic…
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…
In the presence of a boundary interaction, Neumann boundary conditions should be modified to contain a function S of the boundary fields: (\nabla_N +S)\phi =0. Information on quantum boundary dynamics is then encoded in the $S$-dependent…
The first three coefficients in an expansion of the heat kernel of a nonminimal nonabelian kinetic operator taken in an arbitrary background gauge in arbitrary space-time dimension are calculated
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres.…
We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one…
We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel…
We consider a semi-infinite dielectric with multiple spatially dispersive resonances in the susceptibility. The effect of the boundary is described by an arbitrary reflection coefficient for polarization waves in the material at the…
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…
The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…