Heat Invariant E 2 for Nonminimal Operator on Manifolds with Torsion

Abstract

Abstract. Computer algebra methods are applied to investigation of spectral asymptotics of elliptic differential operators on curved manifolds with torsion and in the presence of a gauge field. In this paper we present complete expressions for the second coefficient (E2) in the heat kernel expansion for nonminimal operator on manifolds with nonzero torsion. The expressions were computed for general case of manifolds of arbitrary dimension n and also for the most important for E2 case n = 2. The calculations have been carried out on PC with the help of a program written in C.

Heat trace for Laplace type operators with non-scalar symbols

“…As a first step, we begin to collect all terms B µ 1 ...µ 2p k of (4.4) due to the different variables appearing in (2. 19) and (2.20), including their signs.…”