Canonical Quantization on a Doubly Connected Space and the Aharonov-Bohm Phase

研究成果: ジャーナルへの寄稿学術誌査読

4 被引用数 (Scopus)

抄録

We consider the canonical quantization (Schrödinger representation) on a doubly connected space ΩR≡R2\{(x, y)x2+y2≤R2} (R>0). We show that, when we employ 2-dimensional orthogonal coordinates Ox1x2, there are uncountably many different self-adjoint extensions pUj of pj≡-i∂/∂xj (j=1, 2), and none of the pairs {pj, qj′}j, j′=1, 2 (qj′≡xj′·) satisfies the Weyl relation. Then, we construct a new canonical pair of canonical momentum and position operators so that the pair can satisfy the Weyl relation by using the streamline coordinates. As its application, in the Weyl relation with respect to the pair of the mv-momentum and position operators by the above new canonical pair, we find the Aharonov-Bohm phase.

本文言語英語
ページ(範囲)322-363
ページ数42
ジャーナルJournal of Functional Analysis
174
2
DOI
出版ステータス出版済み - 7月 10 2000
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