SEELEY-GILKEY COEFFICIENTS FOR SUPEROPERATORS

Abstract

Starting from a expansion of exp [-(A0 + A1)t] in powers of A1, we can obtain Seeley-Gilkey coefficients an(x,y) for <x| exp [-H t]|y> when H has dependency on both bosonic and fermionic variables. We consider operators of the form H = p2 + αL·p + p · αR + ϕ(p≡ - i∂) where, in general, αL ≠ αR. To illustrate how these can be used, we compute in closed form the coefficient a1(x,x) and from it the η-function in a three-dimensional model in which a spinor couples to an Abelian vector field with a topological action. The η-function turns out not to have the form of the classical action.