Progress of Theoretical Physics
Supplement No.135 (1999) pp. 244-258
URL : http://ptp.ipap.jp/link?PTPS/135/244/
DOI : 10.1143/PTPS.135.244

Phase-Space Quantization of Field Theory

Cosmas Zachos^* and Thomas Curtright^*,**

(Received March 28, 1999)

In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple — indeed, classical — for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published in Refs. 1) and 2).

^*Speaker. E-mail address: zachos@hep.anl.gov
^**E-mail address: curtright@physics.miami.edu

References:

1. T. Curtright and C. Zachos, J. of Phys. A32 (1999), 771[IoP STACKS].
2. T. Curtright, D. Fairlie and C. Zachos, Phys. Rev. D58 (1998), 025002[APS].
3. E. Wigner, Phys. Rev. 40 (1932), 749[APS].
   For reviews, see:
   M. Hillery, R. O'Conell, M. Scully and E. Wigner, Phys. Rep. 106 (1984), 121[CrossRef].
   H-W. Lee, Phys. Rep. 259 (1995), 147[CrossRef].
   N. Balasz and B. Jennings, Phys. Rep. 104 (1984), 347[CrossRef].
   R. Littlejohn, Phys. Rep. 138 (1986), 193[CrossRef].
   M. Berry, Philos. Trans. R. Soc. London A287 (1977), 237.
   F. Hansen, Publ. RIMS Kyoto Univ. 26 (1990), 885.
   P. Carruthers and F. Zachariasen, Rev. Mod. Phys. 55 (1983), 245[APS].
   L. Cohen, Time-Frequency Analysis (Prentice Hall PTR, Englewood Cliffs, 1995).
4. J. Moyal, Proc. Cambridge Philos. Soc. 45 (1949), 99.
5. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Ann. of Phys. 111 (1978), 61[CrossRef]; ibid. 111 (1978), 111[CrossRef].
6. H. Groenewold, Physica 12 (1946), 405[CrossRef].
7. D. Fairlie, Proc. Cambridge Philos. Soc. 60 (1964), 581.
   D. Fairlie and C. Manogue, J. of Phys. A24 (1991), 3807[IoP STACKS].
   D. Fairlie, Mod. Phys. Lett. A13 (1998), 263.
   Also see:
   K. Takahashi, Prog. Theor. Phys. Suppl. No. 98 (1989), 109[IPAP].
   J. Dahl, in Energy Storage and Redistribution, ed. J. Hinze (Plenum Press, New York, 1983), p. 557.
   L. Cohen, J. Math. Phys. 17 (1976), 1863[AIP Scitation].
   W. Kundt, Z. Naturforschur. a22 (1967), 1333.
8. G. Baker, Phys. Rev. 109 (1958), 2198[APS].
9. T. Takabayasi, Prog. Theot. Phys. 11 (1954), 341.
10. D. Kelly, Phys. Rev. 134 (1964), A641[APS].
    I. Bialinicki-Birula et al., Phys. Rev. D44 (1991), 1825[APS].
    C. Best et al., Ann. of Phys. 225 (1993), 169[CrossRef].
11. A. Pati, Ann. of Phys. 270 (1998), 178[CrossRef].
12. For a review of the relevant features, consider Appendix A in
    T. Curtright, T. Uematsu and C. Zachos, Nucl. Phys. B469 (1996), 488[Elsevier].
13. P. Dirac, Phys. Z. Sowjetunion 3 (1933), 64.
14. G. García-Calderón and M Moshinsky, J. of Phys. A13 (1980), L185[IoP STACKS].
15. J. Vey, Comment Math. Helvet 50 (1975), 412.
    M. Flato, A. Lichnerowicz and D. Sternheimer, J. Math. Phys. 17 (1976), 1754[AIP Scitation].
    M. de Wilde and P. Lecomte, Lett. Math. Phys. 7 (1983), 487.
    P. Fletcher, Phys. Lett. B248 (1990), 323[Elsevier].
16. P. Dirac, Can. J. Math. 2 (1950), 129.
    E. Corrigan and C. Zachos, Phys. Lett. 88B (1979), 273.
17. F. Antonsen, gr-qc/9710021[e-print arXiv].
18. A. M. Ozorio de Almeida, Phys. Rep. 295 (1998), 265[CrossRef].
    J. Klauder and B. Skagerstam, Coherent States (World Scientific, Singapore, 1985).
19. D. Han, Y. Kim and M. Noz, Phys. Rev. A37 (1988), 807[APS].
    Y. Kim and E. Wigner, Phys. Rev. A38 (1988), 1159[APS].
20. M. Bartlett and J. Moyal, Proc. Cambridge Philos. Soc. 45 (1949), 545.
21. B. Lesche, Phys. Rev. D29 (1984), 2270[APS].
22. H. Nachbagauer, hep-th/9703105[e-print arXiv].

Quick Search:

Copyright (c) Progress of Theoretical Physics 1999 All rights reserved.
ptp@yukawa.kyoto-u.ac.jp