de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics
Abstract
We study supersymmetric quantum mechanics on RPn,SO(n),G2 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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