The classical limit in geometric quantization by group extension

被引:0
作者
Bracken, Paul [1 ]
机构
[1] Univ Texas Edinburg, Dept Math, Edinburg, TX 78540 USA
关键词
Group; quantization; Poincar & eacute; Cartan; differential form; group extension; invariant; QUANTUM;
D O I
10.1142/S0219887825501622
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Physical systems as a rule are associated with a symmetry group. The group approach to geometric quantization makes use of this to introduce a quantization by means of group extension. This procedure is discussed and applied to a physical system whose group law has its origin with the Galilean group. The main intention is to investigate the classical limit and its relationship under this approach to geometric quantization. The classical quantization conditions are obtained based on a deeper foundation.
引用
收藏
页数:15
相关论文
共 19 条
[1]  
Abraham R., 1978, Foundations of mechanics
[2]   GROUP FOUNDATIONS OF QUANTUM AND CLASSICAL DYNAMICS - TOWARDS A GLOBALIZATION AND CLASSIFICATION OF SOME OF THEIR STRUCTURES [J].
ALDAYA, V ;
DEAZCARRAGA, JA .
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 1987, 35 (06) :437-473
[3]   COHOMOLOGY, CENTRAL EXTENSIONS, AND (DYNAMICAL) GROUPS [J].
ALDAYA, V ;
DEAZCARRAGA, JA .
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1985, 24 (02) :141-154
[4]   QUANTIZATION AS A CONSEQUENCE OF THE SYMMETRY GROUP - AN APPROACH TO GEOMETRIC-QUANTIZATION [J].
ALDAYA, V ;
DEAZCARRAGA, JA .
JOURNAL OF MATHEMATICAL PHYSICS, 1982, 23 (07) :1297-1305
[5]  
Arnold V. I., 1978, Mathematical methods of classical mechanics
[6]  
ATIYAH M, 1988, PUBL MATH-PARIS, P175
[7]   EXTENSION OF THE CLASSICAL CARTAN FORM [J].
BETOUNES, DE .
PHYSICAL REVIEW D, 1984, 29 (04) :599-606
[8]  
Boya L. J., 1991, Reports on Mathematical Physics, V30, P149, DOI 10.1016/0034-4877(91)90019-J
[9]  
de Azcarraga J., 1998, Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics
[10]   TOPOLOGICAL GAUGE-THEORIES AND GROUP COHOMOLOGY [J].
DIJKGRAAF, R ;
WITTEN, E .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 129 (02) :393-429