Derivation of Mass Spectrum and Magnetic Moments from Current Conservation in Relativistic <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo>(</mo><mn>3</mn><mo>,</mo><mi> </mi><mn>2</mn><mo>)</mo></math></span> and <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo>(</mo><mn>4</mn><mo>,</mo><mi> </mi><mn>2</mn><mo>)</mo></math></span> Theories

A. O. Barut; Dennis Corrigan; Hagen Kleinert

doi:10.1103/PhysRev.167.1527

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Derivation of Mass Spectrum and Magnetic Moments from Current Conservation in Relativistic $O (3, 2)$ and $O (4, 2)$ Theories

A. O. Barut, Dennis Corrigan, and Hagen Kleinert

Department of Physics, University of Colorado, Boulder, Colorado

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Phys. Rev. 167, 1527 – Published 25 March, 1968

DOI: https://doi.org/10.1103/PhysRev.167.1527

Abstract

It is shown that in the framework of the noncompact dynamical group theory, for every choice of the current operator in the representation space, the requirements of current conservation and universality of charge determine the relativistic mass spectrum. The most general currents linear in the algebra and linear in the momenta are investigated, and mass spectra of the form $m = C (j + \frac{1}{2})$ in $O (3, 2)$ , and of the form $m = C n$ or $m = C n {(1 + \frac{a}{n^{2}})}^{\frac{1}{2}}$ in $O (4, 2)$ , are derived with positive magnetic moments and with form factors in agreement with experiment. The freedom in the choice of currents, minimal or nonminimal, is discussed and compared with that which exists in the usual Lagrangian field theory.

References (13)

E. Majorana, Nuovo Cimento 9, 335 (1932)
I. M. Gel'fand and A. M. Yaglom, Zh. Experim. i Teor. Fiz. 18, 703 (1948)
Y. Nambu, Progr. Theoret. Physics Suppl. (Kyoto) 37 & 38, 368 (1966) Phys. Rev. 160, 1171 (1967) T. Takabayashi, Progr. Theoret. Phys. Suppl. (Kyoto), 339 (1965)
P. Budini and C. Fronsdal, Phys. Rev. Letters 14, 968 (1965) C. Frondsal, in High Energy Physics and Elementary Particles (International Atomic Energy Agency, Vienna 1965), p. 665 Phys. Rev. 156, 1653 (1967)
A. O. Barut, in High Energy Physics and Elementary Particles (International Atomic Energy Agency, Vienna 1965), p. 679 A. O. Barut and A. Böhm, Phys. Rev. 139, B1107 (1965) A. Böhm, ibid. 145, 1212 (1966) N. Mukunda, L. O'Raifeartaigh, and E. C. G. Sudarshan, Phys. Rev. Letters 15, 1041 (1965) P. Budini, Nuovo Cimento 44A, 363 (1966) A. O. Barut, Phys. Rev. 156, 1538 (1967) A. O. Barut and H. Kleinert, ibid. 156, 1541 (1967) in Proceedings of the Fourth Coral Gables Conference on Symmetry Principles at High Energies, University of Miami, 1967 (W. H. Freeman and Co., San Francisco, 1967), pp. 70-105
G. Cocho, C. Fronsdal, Harun-Ar-Rashid, and R. White, Phys. Rev. Letters 17, 275 (1966) H. Leuthwyler, ibid. 17, 156 (1966) W. Rühl, Nuovo Cimento 44, 572 (1966)
A. O. Barut and H. Kleinert, Phys. Rev. Letters 18, 754 (1967) H. Kleinert, ibid. 18, 1027 (1967) A. O. Barut and K. C. Tripathy, ibid. 19, 918 (1967) ibid.19, 1081 (1967)
A. O. Barut and H. Kleinert, Phys. Rev. 160, 1149 (1967)
H. Kleinert, Ph.D. thesis, University of Colorado, 1967 (unpublished)
T. Takabayashi, Nagoya University Report, 1967 (unpublished)
S. Ström, Arkiv Fysik 29, 467 (1965)
A. O. Barut and H. Kleinert, Phys. Rev. 161, 1464 (1967)
A. O. Barut, D. Corrigan and H. Kleinert, Phys. Rev. Letters 20, 167 (1968)

[c1] E. Majorana, Nuovo Cimento 9, 335 (1932)

[c2] I. M. Gel'fand and A. M. Yaglom, Zh. Experim. i Teor. Fiz. 18, 703 (1948)

[c3] Y. Nambu, Progr. Theoret. Physics Suppl. (Kyoto) 37 & 38, 368 (1966) Phys. Rev. 160, 1171 (1967) T. Takabayashi, Progr. Theoret. Phys. Suppl. (Kyoto), 339 (1965)

[c4] P. Budini and C. Fronsdal, Phys. Rev. Letters 14, 968 (1965) C. Frondsal, in High Energy Physics and Elementary Particles (International Atomic Energy Agency, Vienna 1965), p. 665 Phys. Rev. 156, 1653 (1967)

[c5] A. O. Barut, in High Energy Physics and Elementary Particles (International Atomic Energy Agency, Vienna 1965), p. 679 A. O. Barut and A. Böhm, Phys. Rev. 139, B1107 (1965) A. Böhm, ibid. 145, 1212 (1966) N. Mukunda, L. O'Raifeartaigh, and E. C. G. Sudarshan, Phys. Rev. Letters 15, 1041 (1965) P. Budini, Nuovo Cimento 44A, 363 (1966) A. O. Barut, Phys. Rev. 156, 1538 (1967) A. O. Barut and H. Kleinert, ibid. 156, 1541 (1967) in Proceedings of the Fourth Coral Gables Conference on Symmetry Principles at High Energies, University of Miami, 1967 (W. H. Freeman and Co., San Francisco, 1967), pp. 70-105

[c6] G. Cocho, C. Fronsdal, Harun-Ar-Rashid, and R. White, Phys. Rev. Letters 17, 275 (1966) H. Leuthwyler, ibid. 17, 156 (1966) W. Rühl, Nuovo Cimento 44, 572 (1966)

[c7] A. O. Barut and H. Kleinert, Phys. Rev. Letters 18, 754 (1967) H. Kleinert, ibid. 18, 1027 (1967) A. O. Barut and K. C. Tripathy, ibid. 19, 918 (1967) ibid.19, 1081 (1967)

[c8] A. O. Barut and H. Kleinert, Phys. Rev. 160, 1149 (1967)

[c9] H. Kleinert, Ph.D. thesis, University of Colorado, 1967 (unpublished)

[c10] T. Takabayashi, Nagoya University Report, 1967 (unpublished)

[c11] S. Ström, Arkiv Fysik 29, 467 (1965)

[c12] A. O. Barut and H. Kleinert, Phys. Rev. 161, 1464 (1967)

[c13] A. O. Barut, D. Corrigan and H. Kleinert, Phys. Rev. Letters 20, 167 (1968)

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Derivation of Mass Spectrum and Magnetic Moments from Current Conservation in Relativistic $O (3, 2)$ and $O (4, 2)$ Theories

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Derivation of Mass Spectrum and Magnetic Moments from Current Conservation in Relativistic O(3, 2) and O(4, 2) Theories

Abstract

References (13)

Derivation of Mass Spectrum and Magnetic Moments from Current Conservation in Relativistic $O (3, 2)$ and $O (4, 2)$ Theories