New Pathways in High-Energy Physics I pp 121-133 | Cite as

# Electric Charge in Composite Magnetic Monopole Theories

## Abstract

It is observed that the spin approach to the interaction of electric charges with magnetic monopoles leads naturally to theories with composite monopoles made from SU(2) gauge fields. The key steps are to express the “electromagnetic field angular momentum” associated with a charge-pole system as a quantum-mechanical spin operator (as was done some years ago) and then to identify this spin operator as the generator of SU(2) transformations on charged-particle wave functions. It is emphasized that composite monopoles may not occur unless electric charge is one of the operators of an SU(2) symmetry. The formalism for conservation of electric charge, and quantization of the electric charge of a monopole, is developed at a “first-quantized” level. Speculations are given on high energy charge-pole scattering. Some problems with second quantization are discussed, and the possibility is raised that there may be an infinite mass renormalization of a composite monopole which has finite mass in the classical approximation.

## Keywords

Gauge Theory Electric Charge Wave Packet Gauge Field Magnetic Monopole## Preview

Unable to display preview. Download preview PDF.

## References

- 1.P. B. Price, E. K. Shirk, W. Z. Osborne and L. S. Pinsky, Phys. Rev. Lett. 35, 487 (1975)CrossRefGoogle Scholar
- P. B. Price, these proceedings.Google Scholar
- 2.H. Poincaré, Compt. Rend. 123, 530 (1896).Google Scholar
- 3.P. A. M. Dirac, Proc. Roy. Soc. (London) A133, 60 (1931).CrossRefGoogle Scholar
- P. A. M. Dirac, these proceedings.Google Scholar
- 4.D. Rosenbaum, Phys. Rev. 147, 891 (1966).CrossRefGoogle Scholar
- 5.A. S. Goldhaber and J. Smith, Rep. Prog. Phys. 38, 731 (1975).CrossRefGoogle Scholar
- 6.A. S. Goldhaber, Phys. Rev. 140, B1407 (1965). In this paper the Hamiltonian in Eq. 2 was written down, and shown to be equivalent to that of Dirac, avoiding the singular string in return for the introduction of 2s redundant components of the wave function. However, H was not recognized as the square of a velocity operator, and the connection with gauge theory described below was not made.Google Scholar
- 7.H. J. Lipkin, W. I. Weisberger and M. Peshkin, Ann. Phys. (N. Y.) 53, 203 (1969).CrossRefGoogle Scholar
- 8.C. N. Yang and R. L. Mills, Phys. Rev. 96, 191 (1954).CrossRefGoogle Scholar
- 9.T. T. Wu and C. N. Yang, in Properties of Matter Under Unusual Conditions, (H. Mark and S. Fernbach, eds., Interscience, N. Y.), 349 (1969). In this work the point monopole gauge field (Eq. 5) was written down, but not recognized as a magnetic pole.Google Scholar
- 10.An elementary consequence of this derivation of the SU(2) gauge field formulation of monopole theory is that the isospin of a single-particle wave function contributes to the total angular momentum. After all, the starting point was,L = k + sti, but from s from the gauge field formalism by R. Jackiw and C. Rebbi in an MIT preprint, “Spin from Isospin in a Gauge Theory,” C. T. P. 524, February, 1976. They refer to a recent preprint by M. Prasad and C. Sommerfield, which I have not seen. A similar observation has been made by P. Hasenfratz and G. t Hooft, Phys. Rev. Lett., in press.Google Scholar
- 11.G. ‘t Hooft, Nuc. Phys. B79, 276 (1974).CrossRefGoogle Scholar
- 12.A. M. Polyakov, ZhETF Pis. Red. 20, 430 (1974).Google Scholar
- M. Polyakov, JETP Lett. 20, 194 (1974).Google Scholar
- 13.There has been some confusion about this because the word “monopole” has been associted with topological properties of constructs which do not produce the Lorentz force of a magnetic pole on an electrically charged particle. From a matter-of-fact point of view then, these SU(3) gauge field solutions have nothing to do with magnetic monopoles, and do not contradict the assertions made here. A. Chakrabarti, Nucl. Phys. B101, 159 (1975)Google Scholar
- W. J. Marciano and H. Pagels, Phys. Rev. D12, l093 (1975).Google Scholar
- W. J. Marciano and H. Pagels, Phys. Rev. D12, l093 (1975).Google Scholar
- 15.B. Julia and A. Zee, Phys. Rev. Dll, 2227 (1975).Google Scholar
- M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975).CrossRefGoogle Scholar
- 16.A. H. Guth has informed me that the charge density operator can be obtained in a straight-forward manner. It is a nonlocal function of deviations from the static monopole gauge field.Google Scholar
- 17.I. Tamm, Z. Phys. 71, 141 (1932).Google Scholar
- 18.P. P. Banderet, Heiv. Phys. Acta 19, 503 (1946).Google Scholar
- 19.T. T. Wu and C. N. Yang, Phys, Rev. D12, 3845 (1975) and to be published. The different regions overlap, and in the overlap of 2 regions both gauges are defined and non-singular. The transformation between the two gauges must be single-valued.Google Scholar