等質空間の量子力学 : 日本語のまえおきつき(マニフォールド上での量子化および量子論)

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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。It is known that there exist an infinite number of inequivalent quantizations on a topologically nontrivial manifold even if it is a finite-dimensional manifold. In this paper we consider the abelian sigma model in (1+1) dimensions to explore a system having infinite degrees of freedom. The model has a field variable φ : S^1 → S^1. An algebra of the quantum field is defined respecting the topological aspect of this model. A central extension of the algebra is also introduced. It is shown that there exist an infinite number of unitary inequivalent representations, which are characterized by a central extension and a continuous parameter α (0*α<1). When the central extension exists, the winding operator and the zero-mode momentum obey a nontrivial commutator.
物性研究刊行会の論文
1996-12-20