Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 322-363 |
| Number of pages | 42 |
| Journal | Journal of Functional Analysis |
| Volume | 174 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jul 10 2000 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Analysis
Cite this
Canonical Quantization on a Doubly Connected Space and the Aharonov-Bohm Phase. / Hirokawa, Masao.
In: Journal of Functional Analysis, Vol. 174, No. 2, 10.07.2000, p. 322-363.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Canonical Quantization on a Doubly Connected Space and the Aharonov-Bohm Phase
AU - Hirokawa, Masao
PY - 2000/7/10
Y1 - 2000/7/10
N2 - 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.
AB - 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.
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U2 - 10.1006/jfan.2000.3591
DO - 10.1006/jfan.2000.3591
M3 - Article
AN - SCOPUS:0347947913
VL - 174
SP - 322
EP - 363
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -