Abstract
We compute for any ordering the star exponentials of all polynomials of degree not greater than two on the 2l -dimensional phase space of a quantum system with l degrees of freedom, and we show in the particular case of the Moyal star product that the Weyl transform of the Moyal star exponential of the one-dimensional harmonic oscillator Hamiltonian is the evolution operator of this quantum system.
REFERENCES
- 1. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer, Ann. Phys.111, 61 (1978). Google ScholarCrossref
- 2. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer, Ann. Phys.111, 111 (1978). Google ScholarCrossref
- 3. J.-M. Maillard, J. Geom. Phys. 3, 231 (1986). Google ScholarCrossref
- 4. F. Bayenand J.-M. Maillard, Lett. Math. Phys. 6, 491 (1982). Google ScholarCrossref
- 5. J. Dito, Lett. Math. Phys. 20, 125 (1990). Google ScholarCrossref
- 6. H. Omori, Y. Maeda, N. Miyazaki, and A. Yoshioka, “Star exponential functions for quadratic forms and polar elements,” in Quantization, Poisson Brackets and Beyond (Manchester, 2001), edited by T. Voronov, Contemp. Math. Vol. 315 (A.M.S., Providence, RI, 2002), pp. 25–38. Google Scholar
- 7. J. Dito, J. Math. Phys. 33, 791 (1992). Google ScholarScitation
- 8. G. S. Agarwaland E. Wolf, Phys. Rev. D 2, 2161 (1970). Google ScholarCrossref
- 9. W. T. Reid: Riccati Differential Equations (Academic, New York, 1972). Google Scholar
- 10. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer-Verlag, Berlin, 1966). Google Scholar
- © 2004 American Institute of Physics.
Please Note: The number of views represents the full text views from December 2016 to date. Article views prior to December 2016 are not included.
