Aharonov-Bohm problem for spin 1

M. L. Horner; Alfred S. Goldhaber

doi:10.1103/PhysRevD.55.5951

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Aharonov-Bohm problem for spin 1

M. L. Horner and Alfred S. Goldhaber

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, United Kingdom
Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794-3840

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Phys. Rev. D 55, 5951 – Published 15 May, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.5951

Abstract

The basic AB problem is to determine how an unshielded tube of magnetic flux $Φ$ affects arbitrarily long-wavelength charged particles impinging on it. For spin 1 at almost all $Φ$ the particles do not penetrate the tube, so the interaction essentially is periodic in $Φ$ (AB effect). Below-threshold bound states move freely only along the tube axis, and consequent induced vacuum currents supplement rather than screen $Φ$ . For a pure magnetic interaction the tube must be broader than the particle Compton wavelength, i.e., only the nonrelativistic spin- $1$ AB problem exists.

References (15)

Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
W. Ehrenberg and R. E. Siday, Proc. Phys. Soc. London, Sec. B 62, 8 (1949), earlier discussed the AB effect, but not the AB problem.
E. M. Serebryanyi, Theor. Math. Phys. 64, 846 (1985).
M. G. Alford, J. March-Russell, and F. Wilczek, Nucl. Phys. B328, 140 (1989); C. R. Hagen, Phys. Rev. Lett. 64, 503 (1990); F. Vera and I. Schmidt, Phys. Rev. D 42, 3591 (1990).
Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461 (1979).
P. Górnicki, Ann. Phys. (N.Y.) 202, 271 (1990).
N. K. Nielsen, Am. J. Phys. 49, 1171 (1981). See also A. S. Goldhaber, H.-N. Li, and R. R. Parwani, Phys. Rev. D 51, 919 (1995).
M. L. Horner and A. S. Goldhaber, Am. J. Phys. 64, 1237 (1996).
C. R. Hagen and S. Ramaswamy, Phys. Rev. D 42, 3524 (1990); C. R. Hagen, Int. J. Mod. Phys. A 6, 3119 (1991).
See, e.g., H. A. Olsen, P. Osland, and T. T. Wu, Phys. Rev. D 42, 665 (1990).
S. L. Glashow, Nucl. Phys. 10, 107 (1959).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).
S. W. MacDowell and O. Törnqvist, Phys. Rev. D 45, 3833 (1992).
H. B. Nielsen and P. Olesen, Nucl. Phys. B160, 380 (1979).
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, England, 1994).

[c1] Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).

[c2] W. Ehrenberg and R. E. Siday, Proc. Phys. Soc. London, Sec. B 62, 8 (1949), earlier discussed the AB effect, but not the AB problem.

[c3] E. M. Serebryanyi, Theor. Math. Phys. 64, 846 (1985).

[c4] M. G. Alford, J. March-Russell, and F. Wilczek, Nucl. Phys. B328, 140 (1989); C. R. Hagen, Phys. Rev. Lett. 64, 503 (1990); F. Vera and I. Schmidt, Phys. Rev. D 42, 3591 (1990).

[c5] Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461 (1979).

[c6] P. Górnicki, Ann. Phys. (N.Y.) 202, 271 (1990).

[c7] N. K. Nielsen, Am. J. Phys. 49, 1171 (1981). See also A. S. Goldhaber, H.-N. Li, and R. R. Parwani, Phys. Rev. D 51, 919 (1995).

[c8] M. L. Horner and A. S. Goldhaber, Am. J. Phys. 64, 1237 (1996).

[c9] C. R. Hagen and S. Ramaswamy, Phys. Rev. D 42, 3524 (1990); C. R. Hagen, Int. J. Mod. Phys. A 6, 3119 (1991).

[c10] See, e.g., H. A. Olsen, P. Osland, and T. T. Wu, Phys. Rev. D 42, 665 (1990).

[c11] S. L. Glashow, Nucl. Phys. 10, 107 (1959).

[c12] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).

[c13] S. W. MacDowell and O. Törnqvist, Phys. Rev. D 45, 3833 (1992).

[c14] H. B. Nielsen and P. Olesen, Nucl. Phys. B160, 380 (1979).

[c15] A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, England, 1994).

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