Authors: Tadafumi Ohsaku
Various geometric aspects of the Nambu-Goldstone ( NG ) type symmetry breakings ( normal, generalized, and anomalous NG theorems ) are summarized, and their relations are discussed. By the viewpoint of Riemannian geometry, Laplacian, curvature and geodesics are examined. Theory of Ricci ow is investigated in complex geometry of the NG-type theorems, and its diusion and stochastic forms are derived. In our anomalous NG theorems, the structure of symplectic geometry is emphasized, Lagrangian submanifolds and mirror duality are noticed. Possible relations between the Langlands correspondence, the Riemann hypothesis and the geometric nature of NG-type theorems are given.
Comments: 63 Pages.
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