TL;DR
This paper explores the relationship between gauge fixing and equivariant cohomology through a supersymmetric model, showing how different gauge choices influence the resulting quantum theories.
Contribution
It provides a detailed analysis of gauge fixing in a supersymmetric model related to equivariant cohomology, highlighting the impact of gauge choices on quantum theories.
Findings
Different gauge-fixing fermions lead to distinct quantum theories
The supersymmetric model reproduces Witten's approach to equivariant cohomology
Gauge fixing intricacies are crucial for understanding the quantum structure
Abstract
The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.
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