13 citations · 17 across the 6 of their papers we have counts for
5 papers · 1 filter
Quantization on a torus without position operators
Shogo Tanimura
We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct ir…
An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian
Makoto Sakamoto, Shogo Tanimura
We solved the Schr{ö}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; t…
Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure
Shogo Tanimura
We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient s…
Zero-mode, Winding Number and Quantization of Abelian Sigma Model in (1+1) Dimensions
Shogo Tanimura
We consider the sigma model in the two dimensional space-time which is a field-theoretical model possessing a nontrivial topology. It is pointed out that its topological s…
Quantum Mechanics on Manifolds
Shogo Tanimura
A definition of quantum mechanics on a manifold is proposed and a method to realize the definition is presented. This scheme is applicable to a homogeneous space $ M = G / H…