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de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics

Kazuto Oshima
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Abstract

We study supersymmetric quantum mechanics on RP_{n},SO(n),G_{2} and U(2) to examine Witten's Morse theory concretely. We confirm the simple instanton picture of the de Rham cohomology that has been given in a previous paper. We use a reflection symmetry of each theory to select the true vacuums. The number of selected vacuums agrees with the de Rham cohomology for each of the above manifolds.

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Kazuto Oshima. 1998-02-09. de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics. https://doi.org/10.1063/1.532242

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