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Geometric quantization
Abstract
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics.We then discuss prequantization, and go into details of the general method of quantization with respect to a polarization using densities and half-forms.This has applications to the theory of unitary group representations and coadjoint orbits.
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Citations
Cited by
Quantum nature of the big bang: Improved dynamics
Ashtekar, A., Pawlowski, T., & Singh, P. (2006) · Physical Review D · doi:10.1103/physrevd.74.084003 · Cited by 1,147
Local symmetries and constraints
Lee, J., & Wald, R. M. (1990) · Journal of Mathematical Physics · doi:10.1063/1.528801 · Cited by 806
Nonperturbative quantum geometries
Jacobson, T., & Smolin, L. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90286-6 · Cited by 283
Quantization of Chern-Simons gauge theory with complex gauge group
Witten, E. (1991) · Communications in Mathematical Physics · doi:10.1007/bf02099116 · Cited by 269
Ashtekar formulation of general relativity and loop-space nonperturbative quantum gravity: a report
Rovelli, C. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/9/002 · Cited by 221
Metadata
- Venue
- Geometric Formulation of Classical and Quantum Mechanics
- Publisher
- WORLD SCIENTIFIC
- Published
- 2010-10
- Pages
- 155-188
- OpenAlex
- W3133809144
- Cited by
- 1,108
- References
- 0
- FWCI
- 149.07
- Type
- book chapter
- Language
- en
- Open access
- closed
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- Geometric quantization. (2010). Geometric Formulation of Classical and Quantum Mechanics. https://doi.org/10.1142/9789814313735_0006
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