Covariant techniques for computation of the heat kernel (original) (raw)

New algorithm for computing the coefficients in the heat kernel expansion

Physics Letters B, 1989

A new covariant method for computing the coefficients in an asymptotic expansion of the heat kernel is suggested. The first two nontrivial coefficients for the second and fourth order minimal differential operators on a riemannian manifold are calculated in an arbitrary space dimension. The algorithmic character of the method suggested allows one to calculate the coefficients by computer using an analytical calculation system.

A method for calculating the heat kernel for manifolds with boundary

arXiv preprint hep-th/9509078, 1995

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 proportional to t 1/2 and t 3/2 are calculated. Our results coincide with completely independent results of previous authors.

A method for calculating the heat kernel for manifolds with a boundary

Physics of Atomic Nuclei, 1993

The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic dierential second order operator is generalized to manifolds with boundary. The rst boundary coecients of the asymptotic expansion which are proportional to t 1=2 and t 3=2 are calculated. Our results coincide with completely independent results of previous authors.

A new algorithm for asymptotic heat kernel expansion for manifolds with boundary

Physics Letters B, 1990

A new algorithm for the computation of the coefficients of the heat kernel expansion, associated with a second-order nonnegative elliptic-symmetric differential operator, defined on an N-dimensional compact riemannian manifold with boundary is presented. Some coefficients are explicitly derived. Using zeta function regularization, an explicit form for the expectation value of the matter stress tensor is given. Corrections to a class of anomalies, due to the presence of the boundary, are found.

Nonperturbative methods for calculating the heat kernel

arXiv preprint hep-th/9602169, 1996

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 into account a finite number of low-order covariant derivatives of the background fields and neglecting all covariant derivatives of higher orders, is proposed. It is shown that a set of covariant differential operators together with the background fields and their low-order derivatives generates a finite dimensional Lie algebra. This algebraic structure can be used to present the heat semigroup operator in the form of an average over the corresponding Lie group. Closed covariant formulas for the heat kernel diagonal are obtained. These formulas serve, in particular, as the generating functions for the whole sequence of the Hadamard-Minakshisundaram-De Witt-Seeley coefficients in all symmetric spaces.

Heat kernel approach in quantum field theory, Nucl. Phys

2013

We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold. We consider both Laplace type operators and non-Laplace type operators on manifolds without boundary as well as Laplace type operators on manifolds with boundary with oblique and non-smooth boundary conditions. Ivan Avramidi: Heat Kernel Approach in Quantum Field Theory 1 1 Effective Action in Gauge Field Theories and Quantum Gravity In this lecture we briefly describe the standard formal construction of the generating functional and the effective action in gauge theories following the covariant spacetime approach to quantum field theory developed mainly by DeWitt [1]. The basic object of any physical theory is the spacetime M, which is assumed to be a m-dimensiona...