Heat Invariant E 2 for Nonminimal Operator on Manifolds with Torsion

Computer algebra methods are applied to the 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 operators on manifolds with nonzero torsion. The expressions were computed for the 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.