相关论文: Spectral functions and their applications

Let $\ui\di$ be the Dirac operator on a $D=2d$ dimensional ball $\mcB$ with radius $R$. We calculate the spectral asymmetry $\eta(0,\ui\di)$ for D=2 and D=4, when local chiral bag boundary conditions are imposed. With these boundary…

We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate several first coefficients of the heat kernel expansion. These coefficients are responsible for divergences and conformal…

For an elliptic differential operator $D$ of order $h$ in $n$ dimensions, the spectral $\zeta$-function $\zeta_D(s)$ for $\Re s > \frac{n}{h}$ can be evaluated as an integral over the heat kernel $e^{-t D}$. Here, alternative expressions…

An asymptotic expansion of the trace of the heat kernel on a cone where the heat coefficients have a delta function behavior at the apex is obtained. It is used to derive the renormalized effective action and total energy of a…

These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof…

We have obtained an explicit expression for the spectral zeta functions and for the heat kernel of strings, drums and quantum billiards working to third order in perturbation theory, using a generalization of the binomial theorem to…

We present an ab initio approach to integration theory for nonunital spectral triples. This is done without reference to local units and in the full generality of semifinite noncommutative geometry. The main result is an equality between…

We compute the full asymptotic expansion of the heat kernel Trace$(\exp(-tD^2))$ where $D$ is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The…

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…

The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes…

The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…

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…

The zeta function associated with higher-spin fields on the Euclidean $4$-ball is investigated. The leading coefficients of the corresponding heat-kernel expansion are given explicitly and the zeta functional determinant is calculated. For…

We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…

A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to…

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…

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…

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…

We discuss modifications in the integral representation of the Riemann zeta-function that lead to generalizations of the Riemann functional equation that preserves the symmetry $s\to (1-s)$ in the critical strip. By modifying one integral…

We consider the ground state energy of a spinor field in the background of a square well shaped magnetic flux tube. We use the zeta- function regularization and express the ground state energy as an integral involving the Jost function of a…