Quantization of Free Spin-Two Fields on the Light Front

Robert G. Root

doi:10.1103/PhysRevD.8.3382

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Quantization of Free Spin-Two Fields on the Light Front

Robert G. Root^*

Physics Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

^*Present address: Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.

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Phys. Rev. D 8, 3382 – Published 15 November, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.3382

Abstract

We show that the free spin-two fields, both massless and massive, can be consistently quantized on a light-front surface, $x^{0} + x^{3} = constant$ . In this formulation, the massless theory is easily shown to be the limit of the massive theory as $m^{2} \to 0$ .

References (18)

P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949)
A. Komar, Phys. Rev. 134, B1430 (1964)
J. B. Kogut and D. E. Soper, Phys. Rev. D 1, 2901 (1970) J. D. Bjorken, J. B. Kogut, and D. E. Soper, ibid. 3, 1382 (1971)
R. A. Neville and F. Rohrlich, Nuovo Cimento 1A, 625 (1971)
T.-M. Yan, Phys. Rev. D 7, 1760 (1973) ibid.7, 1780 (1973)
S.-J. Chang, R. G. Root, and T.-M. Yan, Phys. Rev. D 7, 1133 (1973) S.-J. Chang and T.-M. Yan, ibid. 7, 1147 (1973)
J. Schwinger, Phys. Rev. 91, 713 (1953)
J. Schwinger, Phys. Rev. 127, 324 (1962)
S. Deser [Ann. Phys. (N.Y.) 76, 189 (1973)] H. van Dam and M. Veltman, Nucl. Phys. B22, 397 (1970) D. G. Boulware and S. Deser, Phys. Lett. 40B, 227 (1972) Phys. Rev. D 6, 3368 (1972)
J. D. Bjorken and S. D. Drell [Relativistic Quantum Fields (McGraw-Hill, New York, 1965)]
L. Susskind, Phys. Rev. 165, 1535 (1968)
K. Bardakci and M. B. Halpern, Phys. Rev. 176, 1686 (1968)
S.-J. Chang and S. Ma, Phys. Rev. 180, 1506 (1969)
S.-J. Chang, Phys. Rev. 148, 1259 (1966) Ph.D. thesis, Harvard University, 1967 (unpublished)
R. J. Rivers, Nuovo Cimento 34, 386 (1964)
R. L. Arnowitt, S. Deser, and C. W. Misner, Phys. Rev. 116, 1322 (1959) S. Deser, J. Trubatch, and S. Trubatch, Can. J. Phys. 44, 1715 (1966)
C. Aragone and R. Gambini, Univ. Simon Bolivar, Caracas, Venezuela, Report No. USB/1 (unpublished)
J. Schwinger, Phys. Rev. Lett. 3, 296 (1959)

[c1] P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949)

[c2] A. Komar, Phys. Rev. 134, B1430 (1964)

[c3] J. B. Kogut and D. E. Soper, Phys. Rev. D 1, 2901 (1970) J. D. Bjorken, J. B. Kogut, and D. E. Soper, ibid. 3, 1382 (1971)

[c4] R. A. Neville and F. Rohrlich, Nuovo Cimento 1A, 625 (1971)

[c5] T.-M. Yan, Phys. Rev. D 7, 1760 (1973) ibid.7, 1780 (1973)

[c6] S.-J. Chang, R. G. Root, and T.-M. Yan, Phys. Rev. D 7, 1133 (1973) S.-J. Chang and T.-M. Yan, ibid. 7, 1147 (1973)

[c7] J. Schwinger, Phys. Rev. 91, 713 (1953)

[c8] J. Schwinger, Phys. Rev. 127, 324 (1962)

[c9] S. Deser [Ann. Phys. (N.Y.) 76, 189 (1973)] H. van Dam and M. Veltman, Nucl. Phys. B22, 397 (1970) D. G. Boulware and S. Deser, Phys. Lett. 40B, 227 (1972) Phys. Rev. D 6, 3368 (1972)

[c10] J. D. Bjorken and S. D. Drell [Relativistic Quantum Fields (McGraw-Hill, New York, 1965)]

[c11] L. Susskind, Phys. Rev. 165, 1535 (1968)

[c12] K. Bardakci and M. B. Halpern, Phys. Rev. 176, 1686 (1968)

[c13] S.-J. Chang and S. Ma, Phys. Rev. 180, 1506 (1969)

[c14] S.-J. Chang, Phys. Rev. 148, 1259 (1966) Ph.D. thesis, Harvard University, 1967 (unpublished)

[c15] R. J. Rivers, Nuovo Cimento 34, 386 (1964)

[c16] R. L. Arnowitt, S. Deser, and C. W. Misner, Phys. Rev. 116, 1322 (1959) S. Deser, J. Trubatch, and S. Trubatch, Can. J. Phys. 44, 1715 (1966)

[c17] C. Aragone and R. Gambini, Univ. Simon Bolivar, Caracas, Venezuela, Report No. USB/1 (unpublished)

[c18] J. Schwinger, Phys. Rev. Lett. 3, 296 (1959)

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Quantization of Free Spin-Two Fields on the Light Front

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