On Localization and Regularization

Details On Localization and Regularization On Localization and Regularization

1995-08-24

arxiv.org/abs/hep-th/9508127v1

J.Math.Phys. 37 (1996) 3141-3152

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX

Scientific paper

10.1063/1.531561

Different regularizations are studied in localization of path integrals. We discuss the effect of the choice of regularization by evaluating the partition functions for the harmonic oscillator and the Weyl character for SU(2). In particular, we solve the Weyl shift problem that arises in path integral evaluation of the Weyl character by using the Atiyah-Patodi-Singer $\eta$-invariant and the Borel-Weil theory.

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