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Nontrivial vacua from equal time to the light cone

Kent Hornbostel

  • Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853

Phys. Rev. D 45, 3781 – Published 15 May, 1992

DOI: https://doi.org/10.1103/PhysRevD.45.3781

Abstract

Kinematic arguments suggest that the perturbative vacuum may be an eigenstate of the full Hamiltonian for light-cone-quantized field theories. Nevertheless, properties such as spontaneous symmetry breaking can be accommodated in this approach, by applying a quantization which interpolates between equal-time and light-cone quantization and in which the quantization surface may approach the light cone as a limit. In several simple two-dimensional models presented here, including the Gross-Neveu and Schwinger models, the difference between the full and perturbative vacuum vanishes in this limit. Nonzero vacuum expectation values, however, are preserved by singularities in the fields near k=0. Furthermore, this procedure provides a simple treatment for massless fields and nontrivial tests of Lorentz invariance, and may be applied to models, such as that of Gross and Neveu, for which conventional light-cone quantization is difficult to implement. Finally, the connection between long distances and short times suggests that vacuum effects may be incorporated in an effective Hamiltonian.

References (47)

  1. J. D. Bjorken, J. B. Kogut, and D. E. Soper, Phys. Rev. D 3, 1382 (1971) T.-M. Yan, ibid. 7, 1780 (1972)
  2. S. Weinberg, Phys. Rev. 150, 1313 (1966)
  3. A. P. Zhitnitskii, Yad. Fiz. 43, 1553 (1986) [Sov. J. Nucl. Phys. 43, 999 (1986)]
  4. K. Hornbostel, in From Fundamental Fields to Nuclear Phenomena, edited by J. A. McNeil and C. E. Price (World Scientific, Singapore, 1991)
  5. J. Mathews and R. L. Walker, Mathematical Methods of Physics (Benjamin/Cummings, New York, 1970)
  6. F. Rohrlich, Acta Phys. Aust. 32, 87 (1970)
  7. P. Steinhardt, Ann. Phys. (N.Y.) 128, 425 (1980)
  8. G. McCartor, Z. Phys. C 41, 271 (1988)
  9. Y. Frishman, C. T. Sachrajda, H. Abarbanel, and R. Blankenbecler, Phys. Rev. D 15, 2275 (1977)
  10. D. V. Ahluwalia, in Proceedings of HUGS at CEBAF, edited by W. W. Buck, 1990 (unpublished) D. V. Ahluwalia and D. J. Ernst, Report No. CTP-TAMU 91/90, 1990 (unpublished)
  11. M. S. Sawicki, Phys. Rev. D 44, 433 (1991) Phys. Lett. B 268, 327 (1991)
  12. T. W. Chen, Phys. Rev. D 3, 1989 (1971)
  13. E. Elizalde and J. Gomis, Nuovo Cimento A 35, 367 (1976)
  14. E. V. Prokhvatilov and V. A. Franke, Yad. Fiz. 49, 1109 (1989) [Sov. J. Nucl. Phys. 49, 688 (1989)]
  15. F. Lenz, M. Thies, S. Levit, and K. Yazaki, Ann. Phys. (N.Y.) 208, 1 (1991)
  16. Omitted endnote

  17. A. Harindranath and J. Vary, Phys. Rev. D 37, 3010 (1988)
  18. H.-C. Pauli and S. J. Brodsky, Phys. Rev. D 32, 1993 (1985) ibid.32, 2001 (1985)
  19. D. E. Soper, Ph.D. thesis, SLAC Report No. 137, 1971 (unpublished) H. Leutwyler and J. Stern, Ann. Phys. (N.Y.) 112, 94 (1978)
  20. H. Bergknoff, Nucl. Phys. B122, 215 (1977)
  21. K. Hornbostel, Ph.D. thesis, SLAC Report No. 333, 1988 (unpublished)
  22. S. J. Brodsky and G. P. Lepage, in Perturbative Quantum Chromodynamics, edited by A. H. Mueller (World Scientific, Singapore, 1989) G. P. Lepage, in From Actions to Answers, Proceedings of the TASI-89 Summer School, edited by T. DeGrand and D. Toussiant (World Scientific, Teaneck, NJ, 1990)
  23. R. J. Perry, A. Harindranath, and K. G. Wilson, Phys. Rev. Lett. 65, 2959 (1990)
  24. J. M. Namyslowski, Maryland Report No. MdDP-PP-87-064, 1987 (unpublished)
  25. S. Glazek, Phys. Rev. D 38, 3277 (1988)
  26. T. Eller, H.-C. Pauli, and S. J. Brodsky, Phys. Rev. D 35, 1493 (1987)
  27. M. Burkhardt, Nucl. Phys. A504, 762 (1989)
  28. K. Hornbostel, S. J. Brodsky, and H. C. Pauli, Phys. Rev. D 41, 3814 (1990)
  29. G. 't Hooft, Nucl. Phys. B75, 461 (1974)
  30. C. G. Callan, N. Coote, and D. J. Gross, Phys. Rev. D 13, 1649 (1976)
  31. S.-J. Chang and S.-K. Ma, Phys. Rev. 180, 1506 (1969)
  32. S. D. Drell, D. J. Levy, and T.-M. Yan, Phys. Rev. D 1, 1035 (1970)
  33. S. J. Brodsky, R. Roskies, and R. Suaya, Phys. Rev. D 8, 4574 (1973)
  34. D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974)
  35. M. Thies and K. Ohta [Erlangen report, 1991 (unpublished)]
  36. C. Dietmaier, T. Heinzl, M. Schaden, and E. Werner, Z. Phys. A 334, 215 (1989)
  37. J. Schwinger, Phys. Rev. 128, 2425 (1962)
  38. Y. Nakawaki, Prog. Theor. Phys. 64, 1828 (1980) ibid.70, 1105 (1983)
  39. G. McCartor, Mission Research Corp. report, 1988 (unpublished) Southern Methodist University Report No. SMUTH/91-02, 1991 (unpublished)
  40. K. D. Rothe, H. J. Rothe, and I. O. Stamatescu, Ann. Phys. (N.Y.) 105, 63 (1977)
  41. T. Heinzl, S. Krusche, and E. Werner, Phys. Lett. B 256, 55 (1991)
  42. G. 't Hooft, in New Phenomena in Subnuclear Physics, Proceedings of the 1975 International School of Subnuclear Physics, Erice, Italy, 1975, edited by A. Zichichi, Subnuclear Series Vol. 13A (Plenum, New York, 1977)
  43. N. S. Manton, Ann. Phys. (N.Y.) 159, 220 (1985)
  44. D. A. Uhlenbrock, Commun. Math. Phys. 4, 64 (1967)
  45. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980)
  46. J. H. Lowenstein and J. A. Swieca, Ann. Phys. (N.Y.) 68, 172 (1971) S. Coleman, R. Jackiw, and L. Susskind, ibid. 93, 267 (1975) S. Coleman, ibid. 101, 239 (1976) C. J. Hamer, J. Kogut, D. P. Crewther, and M. M. Mazzolini, Nucl. Phys. B208, 413 (1982) B. E. Baaquie, J. Phys. G 8, 1621 (1982) G. T. Bodwin and E. V. Kovacs, Phys. Rev. D 35, 3198 (1987) ibid.36, 1281 (1987) C. Jayewardena, Helv. Phys. Acta 61, 636 (1988)
  47. [3,15]

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