Quantum Field Theories in the Infinite-Momentum Frame. I. Quantization of Scalar and Dirac Fields

Shau-Jin Chang; Robert G. Root; Tung-Mow Yan

doi:10.1103/PhysRevD.7.1133

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Quantum Field Theories in the Infinite-Momentum Frame. I. Quantization of Scalar and Dirac Fields

Shau-Jin Chang^* and Robert G. Root^*

Tung-Mow Yan^†

Physics Department, University of Illinois, Urbana, Illinois 61801

Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14850

^*Work supported in part by the National Science Foundation under Grant No. NSF GP 25303.
^†Work supported in part by the National Science Foundation.

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Phys. Rev. D 7, 1133 – Published 15 February, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.1133

Abstract

Renormalizable coupled scalar and Dirac field theories are quantized in equal- $x^{+}$ surfaces (called light fronts). Schwinger's action principle is employed to deduce the correct canonical equal- $x^{+}$ (anti-) commutation relations. These theories are shown to be Lorentz-invariant. Generalized Schwinger conditions for a quantum field theory to be Lorentz-invariant are given and discussed in an appendix. Spectral sum rules are derived. Leading singularities of Green's functions and products of field operators near the light cone are studied and the implications to current algebra sum rules are discussed. We also discuss some of the delicate features of the light-front formulation.

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[c1] L. Susskind, Phys. Rev. 165, 1535 (1968)

[c2] K. Bardakci and M. B. Halpern, Phys. Rev. 176, 1686 (1968)

[c3] S.-J. Chang and S. Ma, Phys. Rev. 180, 1506 (1969)

[c4] J. Kogut and D. Soper, Phys. Rev. D 1, 2901 (1970)

[c5] J. D. Bjorken, J. Kogut, and D. Soper, Phys. Rev. D 3, 1382 (1971)

[c6] R. A. Neville and F. Rohrlich, Nuovo Cimento 1A, 625 (1971) Phys. Rev. D 3, 1692 (1971) F. Rohrlich, Acta Phys. Austr. Suppl. 8, 277 (1971)

[c7] [P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949)] P. A. M. Dirac[6], "null-plane." A. Komar, Phys. Rev. 134, B1430 (1964) G. Domokos, Phys. Rev. D 4, 3708 (1971)

[c8] S. Weinberg, Phys. Rev. 150, 1313 (1966)

[c9] R. F. Dashen and M. Gell-Mann, in Proceedings of the Third Coral Gables Conference on Symmetry Principles at High Energies, University of Miami, 1966, edited by A. Perlmutter, J. Wojtaszek, E. C. G. Sudarshan, and B. Kurşunoğlu (Freeman, San Francisco, 1966) S. Fubini, Nuovo Cimento 34A, 475 (1966)

[c10] S. D. Drell, D. J. Levy, and T.-M. Yan, Phys. Rev. 187, 2159 (1969) S. D. Drell and T.-M. Yan, Ann. Phys. (N.Y.) 66, 578 (1971)

[c11] S.-J. Chang and S. Ma, Phys. Rev. 188, 2385 (1969) S.-J. Chang and P. M. Fishbane, Phys. Rev. D 2, 1104 (1970) ibid.3, 1047 (1971)

[c12] H. Fritzsch and M. Gell-Mann, in Broken Scale Invariance and the Light Cone, 1971 Coral Gables Conference on Fundamental Interactions at High Energy, edited by M. Dal Cin, G. J. Iverson, and A. Perlmutter (Gordon and Breach, New York, 1971), Vol. 2, p. 1 D. J. Gross and S. Treiman, Phys. Rev. D 4, 1059 (1971) J. Cornwall and R. Jackiw, ibid. 4, 367 (1971) D. A. Dicus, R. Jackiw, and V. Teplitz, ibid. 4, 1733 (1971) R. Jackiw (unpublished) R. A. Brandt, Phys. Rev. D 1, 2808 (1970) R. A. Brandt and G. Preparata, Nucl. Phys. B27, 541 (1971)

[c13] T.-M. Yan, Phys. Rev. D (to be published) Kogut and Soper ([4]) Cornwall and Jackiw ([12])

[c14] J. Schwinger, Phys. Rev. 82, 914 (1951) ibid.91, 713 (1953)

[c15] J. Schwinger, Proc. Natl. Acad. Sci. U. S. 37, 452 (1951)

[c16] S.-J. Chang and T.-M. Yan, the following paper, Phys. Rev. D 7, 1147 (1973)

[c17] J. Schwinger, Phys. Rev. 127, 324 (1962)

[c18] J. Schwinger, Phil. Mag. 44, 1171 (1953)

[c19] J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)

[c20] Omitted endnote

[c21] Gross and Treiman ([12]) [13]

[c22] S. L. Adler, Phys. Rev. Letters 14, 1051 (1965) Phys. Rev. 140, B736 (1965)

[c23] W. I. Weisberger, Phys. Rev. Letters 14, 1047 (1965) Phys. Rev. 143, 1302 (1966)

[c24] S. L. Adler, Phys. Rev. 143, 1144 (1966)

[c25] Cornwall and Jackiw, Brandt, and Brandt and Preparata[12] , [12]

[c26] Dicus, Jackiw, and Teplitz, [12]

[c27] S. L. Adler and W.-K. Tung, Phys. Rev. Letters 22, 978 (1969) R. Jackiw and G. Preparata, ibid. 22, 975 (1969)

[c28] J. D. Bjorken, Phys. Rev. 179, 1547 (1969)

[c29] S. D. Drell and T. D. Lee [Phys. Rev. D 5, 1738 (1972)]

[c30] G. Calucci, R. Jengo, G. Furlan, and C. Rebbi, Phys. Letters 37B, 416 (1971) Dicus, Jackiw, and Teplitz ([12]), Appendix D

[c31] W. K. Burton and B. F. Touschek, Phil. Mag. 44, 161 (1953)

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Quantum Field Theories in the Infinite-Momentum Frame. I. Quantization of Scalar and Dirac Fields

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See Also

Quantum Field Theories in the Infinite-Momentum Frame. II. Scattering Matrices of Scalar and Dirac Fields

Quantum Field Theories in the Infinite-Momentum Frame. IV. Scattering Matrix of Vector and Dirac Fields and Perturbation Theory

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