De Rham Cohomology of SO(n) by Supersymmetric Quantum Mechanics
Kazuto Oshima
TL;DR
This paper provides an elementary derivation of the de Rham cohomology of SO(n) using supersymmetric quantum mechanics and Morse theory, highlighting reflection symmetries to identify true vacuums that match cohomology.
Contribution
It introduces a novel elementary approach to compute the de Rham cohomology of SO(n) via supersymmetric quantum mechanics and Morse theory, emphasizing reflection symmetries.
Findings
Number of vacuums matches de Rham cohomology of SO(n)
Reflection symmetries help identify true vacuums
Method offers an elementary derivation of topological invariants
Abstract
We give an elementary derivation of the de Rham cohomology of SO(n) in terms of supersymmetric quantum mechanics. Our analysis is based on Witten's Morse theory. We show reflection symmetries of the theory are useful to select true vacuums. The number of the selected vacuums will agree with the de Rham cohomology of SO(n).
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