Coherent State Method in Geometric Quantization

2005 ◽  
pp. 47-78
Author(s):  
Anatol Odzijewicz
Keyword(s):  
Coherent State ◽  
Geometric Quantization ◽  
State Method

scholarly journals Geometric quantization, complex structures and the coherent state transform

2005 ◽  
Vol 221 (2) ◽  
pp. 303-322 ◽  
Author(s):  
Carlos Florentino ◽  
Pedro Matias ◽  
José Mourão ◽  
João P. Nunes
Keyword(s):  
Coherent State ◽  
Geometric Quantization ◽  
Complex Structures

scholarly journals QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS

2005 ◽  
Vol 17 (04) ◽  
pp. 391-490 ◽  
Author(s):  
S. TWAREQUE ALI ◽  
MIROSLAV ENGLIŠ
Keyword(s):  
Quantum Mechanics ◽  
Coherent State ◽  
Deformation Quantization ◽  
Degrees Of Freedom ◽  
Geometric Quantization ◽  
Canonical Quantization ◽  
Open Problems ◽  
General Picture ◽  
The Subject

This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom) including in particular canonical quantization and the related Dirac scheme, introduced in the early days of quantum mechanics, Segal and Borel quantizations, geometric quantization, various ramifications of deformation quantization, Berezin and Berezin–Toeplitz quantizations, prime quantization and coherent state quantization. We have attempted to give an account sufficiently in depth to convey the general picture, as well as to indicate the mutual relationships between various methods, their relative successes and shortcomings, mentioning also open problems in the area. Finally, even for approaches for which lack of space or expertise prevented us from treating them to the extent they would deserve, we have tried to provide ample references to the existing literature on the subject. In all cases, we have made an effort to keep the discussion accessible both to physicists and to mathematicians, including non-specialists in the field.

scholarly journals SPIN-STATISTICS THEOREM AND GEOMETRIC QUANTIZATION

2004 ◽  
Vol 19 (05) ◽  
pp. 655-676 ◽  
Author(s):  
CHARIS ANASTOPOULOS
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
Geometric Quantization ◽  
Continuous Spin ◽  
Joint System ◽  
Symmetry Transformations ◽  
Suitable Change ◽  
Exotic Systems ◽  
State Path ◽  
Internal Symmetries

We study the relation of the spin-statistics theorem to the geometric structures on phase space, which are introduced in quantization procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the nonrelativistic domain (in fact for any symmetry group including internal symmetries) by requiring that the exchange can be implemented smoothly by a class of symmetry transformations that project in the phase space of the joint system system. We discuss the interpretation of this requirement, stressing the fact that any distinction of identical particles comes solely from the choice of coordinates — the exchange then arises from suitable change of coordinate system. We then examine our construction in the geometric and the coherent-state-path-integral quantization schemes. In the appendix we apply our results to exotic systems exhibiting continuous "spin" and "fractional statistics." This gives novel and unusual forms of the spin-statistics relation.

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