Gunma-Tech-98-02 de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics
نویسنده
چکیده
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.
منابع مشابه
de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics
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 man-ifolds.
متن کاملDe Rham Cohomology of SO(n) by Supersymmetric Quantum Mechanics
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).
متن کاملInstanton effects and Witten complex in supersymmetric quantum mechanics on SO(4)
We examine supersymmetric quantum mechanics on SO(4) to realize Witten's idea. We find instanton solutions connecting approximate vacuums. We calculate Hessian matrices for these solutions to determine true vacuums. Our result is in agreement with de Rham cohomology of SO(4). We also give a criterion for cancellation of instanton effects for a pair of instanton paths.
متن کاملOn Quantum De Rham Cohomology Theory
We define the quantum exterior product ∧h and quantum exterior differential dh on Poisson manifolds. The quantum de Rham cohomology, which is a deformation quantization of the de Rham cohomology, is defined as the cohomology of dh. We also define the quantum Dolbeault cohomology. A version of quantum integral on symplectic manifolds is considered and the corresponding quantum Stokes theorem is ...
متن کاملFrobenius Manifolds from Hyperk
We construct a dGBV algebra from Dolbeault complex of any closed hyperkk ahler manifold. A Frobenius manifold structure on an neighborhood of the origin in Dolbeault cohomology then arises via Manin's generalization of Barannikov-Kontsevich's construction of formal Frobenius manifold structure on formal extended moduli space of a Calabi-Yau manifold. It is explained why these two kinds of forma...
متن کامل