Evaluation of the heat kernel in Riemann - Cartan space using the covariant Taylor expansion method

Abstract

In order to evaluate the asymptotic expansion coefficients of the heat kernel associated with a fermion of spin in an arbitrary dimensional Riemann - Cartan spacetime, the limit of application of the covariant Taylor expansion method (Avramidi I G 1989 Teor. Mat. Fiz. 79 219) to the heat kernel is extended. The first three coefficients in the approach are manifestly computed. In the case of a massless fermion of spin coupled to a vector gauge field in six-dimensional Riemann - Cartan spacetime, the third coefficient which is intimately connected with some anomalies is expressed in the form of arranging it with respect to an irreducible -matrix basis.