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The canonical quantization of Dirac field in a finite volume is studied. Following the idea of taking the boundary conditions as primary Dirac constraints, we propose a method to treat both the intrinsic constraints and boundary conditions equally. We shall work in the discrete version and quantize the model canonically. In order to verify our method to treat the intrinsic constraints and boundary conditions on the same footing, we obtain the same results by choosing two different subsets of constraints to construct the intermediate Dirac brackets.
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Keywords:
- boundary conditions /
- Dirac constraints /
- Dirac brackets
[1] Sheikh-Jabbari M M, Shirzad A 2001 Eur. Phys. J. C 19 383
[2] Jing J 2005 Phys. Rev. D 71 025023
[3] Gitman D M, Tyutin I V 1990 Quantization of Fields with Constraints (1st Ed.) (New York: Springer) p276
[4] Jing J, Long Z W 2005 Phys. Rev. D 72 126002
[5] Chu C S, Ho P M 1999 Nucl. Phys. B 550 151
[6] Chu C S, Ho P M 2000 Nucl. Phys. B 568 447
[7] Ardalan F, Arfaei H, Sheikh-Jabbari M M 2000 Nucl. Phys. B 576 578
[8] Long Z W, Chen L 2007 High Energy Phys. and Nucl. Phys. 31 14 (in Chinese) [隆正文, 陈琳 2007 高能物理与核物理 31 14]
[9] Long Z W, Liu B, Li Z P 2004 Acta Phys. Sin. 53 2094 (in Chinese) [隆正文, 刘波, 李子平 2004 53 2094]
[10] Long Z W, Liu B, Li Z P 2003 High Energy Phys. and Nucl. Phys. 27 866 (in Chinese) [隆正文, 刘波, 李子平 2003 高能物理与核物理 27 866]
[11] Jing J 2006 Phys. Rev. D 73 086001
[12] Henneaux M, Teitelboim C 1992 Quantization of Gauge Systems (1st Ed.) (Princeton: Princeton University Press) p134
[13] Faddeev L D, Jackiw R 1988 Phys. Rev. Lett. 60 1692
[14] Dirac P A M 1964 Lecture Notes on Quantum Mechanics (1st Ed.) (New York: Yeshiva University) p8
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[1] Sheikh-Jabbari M M, Shirzad A 2001 Eur. Phys. J. C 19 383
[2] Jing J 2005 Phys. Rev. D 71 025023
[3] Gitman D M, Tyutin I V 1990 Quantization of Fields with Constraints (1st Ed.) (New York: Springer) p276
[4] Jing J, Long Z W 2005 Phys. Rev. D 72 126002
[5] Chu C S, Ho P M 1999 Nucl. Phys. B 550 151
[6] Chu C S, Ho P M 2000 Nucl. Phys. B 568 447
[7] Ardalan F, Arfaei H, Sheikh-Jabbari M M 2000 Nucl. Phys. B 576 578
[8] Long Z W, Chen L 2007 High Energy Phys. and Nucl. Phys. 31 14 (in Chinese) [隆正文, 陈琳 2007 高能物理与核物理 31 14]
[9] Long Z W, Liu B, Li Z P 2004 Acta Phys. Sin. 53 2094 (in Chinese) [隆正文, 刘波, 李子平 2004 53 2094]
[10] Long Z W, Liu B, Li Z P 2003 High Energy Phys. and Nucl. Phys. 27 866 (in Chinese) [隆正文, 刘波, 李子平 2003 高能物理与核物理 27 866]
[11] Jing J 2006 Phys. Rev. D 73 086001
[12] Henneaux M, Teitelboim C 1992 Quantization of Gauge Systems (1st Ed.) (Princeton: Princeton University Press) p134
[13] Faddeev L D, Jackiw R 1988 Phys. Rev. Lett. 60 1692
[14] Dirac P A M 1964 Lecture Notes on Quantum Mechanics (1st Ed.) (New York: Yeshiva University) p8
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