Symbol calculus and zeta--function regularized determinants

Details Symbol calculus and zeta--function regularized determinants Symbol calculus and zeta--function regularized determinants

2007-07-11

arxiv.org/abs/0707.1576v2

J.Math.Phys.48:113501,2007

Physics

Mathematical Physics

Added references, some typos corrected, published version

Scientific paper

10.1063/1.2801883

In this work, we use semigroup integral to evaluate zeta-function regularized determinants. This is especially powerful for non--positive operators such as the Dirac operator. In order to understand fully the quantum effective action one should know not only the potential term but also the leading kinetic term. In this purpose we use the Weyl type of symbol calculus to evaluate the determinant as a derivative expansion. The technique is applied both to a spin--0 bosonic operator and to the Dirac operator coupled to a scalar field.

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