Zero-mode, winding number and commutators of abelian sigma model in (1+1) dimensions : 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,研究会報告)

概要

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It is known that there exist an infinite, number of inequivalent quantizations on a topologically nontrivial manifold even if it is a finitedimensional 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 a α(0 ≤ α < 1). When the central extension exists, the winding operator and the zero-mode momentum obey a nontrivial commutator.
素粒子論グループ素粒子研究編集部の論文
1996-10-20