相关论文: Heat Expansion and Zeta

We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this expansion by a natural intertwining property. In particular we will give a closed formula for…

We study the asymptotic expansion of the smeared L2-trace of fexp(-tP^2) where P is an operator of Dirac type, f is an auxiliary smooth smearing function which is used to localize the problem, and chiral bag boundary conditions are imposed.…

We consider the heat equation $u_t=Lu$ where $L$ is a second-order difference operator in a discrete variable $n$. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients…

We study the spectral properties of the Laplace type operator on the circle. We discuss various approximations for the heat trace, the zeta function and the zeta-regularized determinant. We obtain a differential equation for the heat kernel…

We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the…

We give a complete classification and present new exotic phenomena of the meromorphic structure of $\zeta$-functions associated to general self-adjoint extensions of Laplace-type operators over conic manifolds. We show that the meromorphic…

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…

By applying the covariant Taylor expansion method, the fifth lower coefficients the asymptotic expansion of the heat kernel associated with a fermion of spin 1/2 in Riemann-Cartan space are manifestly given. These coefficients in…

We consider the Hodge Laplacian on manifolds with incomplete edge singularities, with infinite dimensional von Neumann spaces and intricate elliptic boundary value theory. We single out a class of its algebraic self-adjoint extensions. Our…

The off-diagonal heat-kernel expansion of a Laplace operator including a general gauge-connection is computed on a compact manifold without boundary up to third order in the curvatures. These results are used to study the early-time…

We compute the coefficients in asymptotics of regularized traces and associated trace (spectral) distributions for Schrodinger operators, with short and long range potentials. A kernel expansion for the Schrodinger semigroup is derived, and…

We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…

Let $G$ be a compact connected Lie group equipped with a bi-invariant metric. We calculate the asymptotic expansion of the heat kernel of the laplacian on $G$ and the heat trace using Lie algebra methods. The Duflo isomorphism plays a key…

One of the many problems to which J.S. Dowker devoted his attention is the effect of a conical singularity in the base manifold on the behavior of the quantum fields. In particular, he studied the small-$t$ asymptotic expansion of the…

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…

We investigate the short-time expansion of the heat kernel of a Laplace type operator on a compact Riemannian manifold and show that the lowest order term of this expansion is given by the Fredholm determinant of the Hessian of the energy…

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 method which allows for asymptotic expansion of the one-loop effective action W=ln det A is formulated. The positively defined elliptic operator A= U + M^2 depends on the external classical fields taking values in the Lie algebra of the…

Let $\Omega$ be a $C^\infty$-smooth bounded domain of $\mathbb{R}^n$, $n \geq 1$, and let the matrix ${\bf a} \in C^\infty (\overline{\Omega};\R^{n^2})$ be symmetric and uniformly elliptic. We consider the $L^2(\Omega)$-realization $A$ of…

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…