Generalization of geometry-induced effect noted by Takagi and Tanzawa

Abstract

The formulation on a particle motion in n-demensional curved manifold M_n embedded in p-dimensional Euclidean space R_p is summarized, and the geometry-induced gauge structure is explained. Next we examine the scalar field theory with a soliton solution, and point out that in spite of the infinite degrees of freedom such a field theory has the same mathematical structure as a particle motion in M_n ⊂ R_p, and our formalism affords a clearer view of understanding physical contents of such a field theory.