Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 3, 2004, Pages

  Montesinos, Merced ^a   Torres Del Castillo, G F ^b  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

^b BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; FUNCTIONS; HAMILTONIANS; HARMONIC ANALYSIS; OSCILLATORS (ELECTRONIC); POISSON DISTRIBUTION;

HARMONIC OSCILLATOR; QUANTIZATION; QUANTUM DYNAMICS;

QUANTUM THEORY;

EID: 19644401453     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.032104     Document Type: Article

References (16)

1. R. Berndt, An Introduction to Symplectic Geometry (American Mathematical Society, Providence, RI, 2001).
2. P. J. Olver, Applications of Lie Groups to Differential Equations, 2nd ed. (Springer-Verlag, New York, 1993).
3. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (revised) (Oxford University Press, Oxford, 1981).
4. W. Heisenberg, The Physical Principles of the Quantum Theory (University of Chicago Press, Chicago, 1930).
5. W. Heisenberg, "The Development of Quantum Mechanics," Nobel Lecture, 1933 at http://www.nobel.se
6. See, for instance, Mathematics of Contemporary Physics, edited by R. F. Streater (Academic, London, 1972); C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics (Springer, New York, 1967); G. Lion and M. Vergne, The Weil Representation, Maslov Index and Theta Series, Prog. Math. Vol. 6 (Birkhäuser, Basel, 1980).
7. See, for instance, Mathematics of Contemporary Physics, edited by R. F. Streater (Academic, London, 1972); C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics (Springer, New York, 1967); G. Lion and M. Vergne, The Weil Representation, Maslov Index and Theta Series, Prog. Math. Vol. 6 (Birkhäuser, Basel, 1980).
8. See, for instance, Mathematics of Contemporary Physics, edited by R. F. Streater (Academic, London, 1972); C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics (Springer, New York, 1967); G. Lion and M. Vergne, The Weil Representation, Maslov Index and Theta Series, Prog. Math. Vol. 6 (Birkhäuser, Basel, 1980).
9. N. Woodhouse, Geometric Quantization (Oxford University Press, Oxford, 1980); M. Puta, Hamiltonian Mechanical Systems and Geometrie Quantization (Kluwer Academic, Dordrecht, 1993).
10. N. Woodhouse, Geometric Quantization (Oxford University Press, Oxford, 1980); M. Puta, Hamiltonian Mechanical Systems and Geometrie Quantization (Kluwer Academic, Dordrecht, 1993).
11. G. F. Torres del Castillo and G. Mendoza Torres, Rev. Mex. Fís. 49, 445 (2003).
12. G. F. Torres del Castillo and M. P. Velázquez-Quesada, Rev. Mex. Fís. (to be published).
13. G. F. Torres del Castillo and E. Galindo Linares, Rev. Mex. Fís. 49, 344 (2003).
14. M. Montesinos, Phys. Rev. A 68, 014101 (2003).
15. M. Mondragón and M. Montesinos, Int. J. Mod. Phys. A 19, 2473 (2004).
16. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1993).