Quantum mechanics on Riemannian Manifold in Schwinger's Quantization Approach II

Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation group. Using the identification of $M$ with the quotient space $G/H$, where $H$ is the isotropy group of an arbitrary fixed point of $M$, we show that quantum mechanics on $G/H$ possesses a gauge structure, described by the gauge potential that is the connection 1-form of the principal fiber bundle $G(G/H, H)$. The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of states are developed.Comment: 18pages, no figures, LaTe

Equivalence between Schwinger and Dirac schemes of quantization

This paper introduces the modified version of Schwinger's quantization method, in which the information on constraints and the choice of gauge conditions are included implicitly in the choice of variations used in quantization scheme. A proof of equivalence between Schwinger- and Dirac-methods for constraint systems is given.Comment: 12pages, No figures, Latex, The proof is improved and one reference is adde

Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher Dimensional Space

We explain in a context different from that of Maraner the formalism for describing motion of a particle, under the influence of a confining potential, in a neighbourhood of an n-dimensional curved manifold M^n embedded in a p-dimensional Euclidean space R^p with p >= n+2. The effective Hamiltonian on M^n has a (generally non-Abelian) gauge structure determined by geometry of M^n. Such a gauge term is defined in terms of the vectors normal to M^n, and its connection is called the N-connection. In order to see the global effect of this type of connections, the case of M^1 embedded in R^3 is examined, where the relation of an integral of the gauge potential of the N-connection (i.e., the torsion) along a path in M^1 to the Berry's phase is given through Gauss mapping of the vector tangent to M^1. Through the same mapping in the case of M^1 embedded in R^p, where the normal and the tangent quantities are exchanged, the relation of the N-connection to the induced gauge potential on the (p-1)-dimensional sphere S^{p-1} (p >= 3) found by Ohnuki and Kitakado is concretely established. Further, this latter which has the monopole-like structure is also proved to be gauge-equivalent to the spin-connection of S^{p-1}. Finally, by extending formally the fundamental equations for M^n to infinite dimensional case, the present formalism is applied to the field theory that admits a soliton solution. The resultant expression is in some respects different from that of Gervais and Jevicki.Comment: 52 pages, PHYZZX. To be published in Int. J. Mod. Phys.

Manifestation of the Fermi resonance in surface polariton spectra

The method of disturbed full internal reflection (DFIR) is used to detect and interpret the resonance splitting of the surface polariton. The effect in the spectra of oscillatory SP which are reflected by the DFIR method in Otto geometry was experimentally recorded. It is concluded that the resonance splitting of the dispersion branch of SP may serve as an effective method for detecting weak oscillations and for measuring their parameters

Generalization of geometry-induced effect noted by Takagi and Tanzawa

この論文は国立情報学研究所の電子図書館事業により電子化されました。研究会報告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