Derivation of Index Theorems by Localization of Path Integrals
Antero Hietam\"aki
TL;DR
This paper reviews how localization techniques can be used to derive important index theorems, such as Atiyah-Singer and Callias, by exactly computing supersymmetric path integrals.
Contribution
It introduces a novel application of localization methods to derive classical index theorems through supersymmetric path integral calculations.
Findings
Exact derivations of Atiyah-Singer and Callias index theorems
Demonstration of localization method effectiveness in mathematical physics
Connection between supersymmetry and topological invariants
Abstract
We review the derivation of the Atiyah-Singer and Callias index theorems using the recently developed localization method to calculate exactly the relevant supersymmetric path integrals. (Talk given at the III International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 13-24, 1993)
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