Non-Laplace type Operators on Manifolds with Boundary

Details Non-Laplace type Operators on Manifolds with Boundary Non-Laplace type Operators on Manifolds with Boundary

2005-09-12

arxiv.org/abs/math-ph/0509023v3

Analysis, Geometry and Topology of Elliptic Operators, Eds. B. Booss-Bavnbek, S. Klimek, M. Lesch and W. Zhang (Singapore: Wor

Physics

Mathematical Physics

Introduction and bibliography significantly expanded. 39 pages, no figures, to be published in: Proceedings of the Workshop ``

Scientific paper

We study second-order elliptic partial differential operators acting on sections of vector bundles over a compact manifold with boundary with a non-scalar positive definite leading symbol. Such operators, called non-Laplace type operators, appear, in particular, in gauge field theories, string theory as well as models of non-commutative gravity theories, when instead of a Riemannian metric there is a matrix valued self-adjoint symmetric two-tensor that plays the role of a ``non-commutative'' metric. It is well known that there is a small-time asymptotic expansion of the trace of the corresponding heat kernel in half-integer powers of time. We initiate the development of a systematic approach for the explicit calculation of these coefficients, construct the corresponding parametrix of the heat equation and compute explicitly the first two heat trace coefficients.

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