Relativistic quantum transport theory approach to multiparticle production

P. Carruthers; F. Zachariasen

doi:10.1103/PhysRevD.13.950

Access by Xinjiang University

Relativistic quantum transport theory approach to multiparticle production

P. Carruthers^*

F. Zachariasen^†

Theoretical Division, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544

California Institute of Technology, Pasadena, California 91125

^*Research performed under the auspices of the U. S. Energy Research and Development Administration.
^†Work supported in part by the Energy Research and Development Administration under Contract No. AT (11-1)-68 for the San Francisco Operations Office.

PDF

Phys. Rev. D 13, 950 – Published 15 February, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.950

Abstract

The field-theoretic description of multiparticle production processes is cast in a form analogous to ordinary transport theory. Inclusive differential cross sections are shown to be given by integrals of covariant phasespace distributions. The single-particle distribution function $F (p, R)$ is defined as the Fourier transform of a suitable correlation function in analogy with the nonrelativistic (Wigner) phase-space distribution function. Its transform $F (p, q)$ is observed to be essentially the discontinuity of a multiparticle scattering amplitude. External-field problems are studied to exhibit the physical content of the formalism. When $q = 0$ one recovers the single-particle distribution exactly. The equation of motion for $F (p, R)$ generates an infinite hierarchy of coupled equations for various distribution functions. In the Hartree approximation one obtains nonlinear integral equations analogous to the Vlasov equation in plasma physics. Such equations are convenient for exhibiting collective motions; in particular it appears that a collective mode exists in a $φ^{4}$ theory for a uniform infinite medium. It is speculated that such collective modes could provide a theoretical basis for clustering effects in multiparticle production.

References (13)

AIP Conference Proceedings No. 23, Particles and Fields Subseries No. 10, edited by Carl E. Carlson (American Institute of Physics, New York, 1975) Theories and Experiments in High-Energy Physics, proceedings of the second Orbis Scientiae Univ. of Miami, 1975, edited by A. Perlmutter and S. M. Widmayer (Plenum, New York, 1975)
F. Cooper and D. Sharp [in proceedings of Orbis Scientiae II, Coral Gables, 1975 (unpublished) Phys. Rev. D 12, 1123 (1975)]
R. Brout and P. Carruthers, Lectures on the Many-Electron Problem (Interscience, New York, 1963), Chap. 1
T. Ludlam and R. Slansky, Phys. Rev. D 8, 1408 (1973)
W. Kittel, S. Ratti, and L. Van Hove, Nucl. Phys. B30, 333 (1971)
E. Wigner, Phys. Rev. 40, 749 (1932)
J. Ross and K. Kirkwood, J. Chem. Phys. 22, 1094 (1954)
J. H. Irving and R. W. Zwanzig, J. Chem. Phys. 19, 1173 (1951)
E. Remler and A. P. Sathe, Ann. Phys. (N.Y.) (to be published)
L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962)
J. H. Irving, Ph.D. thesis, Princeton Univ., 1967 (unpublished)
A. Mueller, Phys. Rev. D 2, 2963 (1970)
L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974)

[c1] AIP Conference Proceedings No. 23, Particles and Fields Subseries No. 10, edited by Carl E. Carlson (American Institute of Physics, New York, 1975) Theories and Experiments in High-Energy Physics, proceedings of the second Orbis Scientiae Univ. of Miami, 1975, edited by A. Perlmutter and S. M. Widmayer (Plenum, New York, 1975)

[c2] F. Cooper and D. Sharp [in proceedings of Orbis Scientiae II, Coral Gables, 1975 (unpublished) Phys. Rev. D 12, 1123 (1975)]

[c3] R. Brout and P. Carruthers, Lectures on the Many-Electron Problem (Interscience, New York, 1963), Chap. 1

[c4] T. Ludlam and R. Slansky, Phys. Rev. D 8, 1408 (1973)

[c5] W. Kittel, S. Ratti, and L. Van Hove, Nucl. Phys. B30, 333 (1971)

[c6] E. Wigner, Phys. Rev. 40, 749 (1932)

[c7] J. Ross and K. Kirkwood, J. Chem. Phys. 22, 1094 (1954)

[c8] J. H. Irving and R. W. Zwanzig, J. Chem. Phys. 19, 1173 (1951)

[c9] E. Remler and A. P. Sathe, Ann. Phys. (N.Y.) (to be published)

[c10] L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962)

[c11] J. H. Irving, Ph.D. thesis, Princeton Univ., 1967 (unpublished)

[c12] A. Mueller, Phys. Rev. D 2, 2963 (1970)

[c13] L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974)

Physical Review D

Export citation

Export citation

Relativistic quantum transport theory approach to multiparticle production

Abstract

References (13)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation