Abstract
For a Minkowski spacetime of dimension three, particles of arbitrary, real spin and intermediate (ϑ-) statistics, called ‘anyons’, are studied within the framework of relativistic quantum field theory. The localization properties of interpolating fields for anyons and the relation between the spin of anyons and their statistics are discussed on general grounds. A model of a quantum field theory exhibiting anyons is described. Our results might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of high-T c superconductors.
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References
Wilczek, F., Phys. Rev. Lett. 48, 1144 (1982); 49, 957 (192); see also: Wilczek, F. and Zee, A., Phys. Rev. Lett. 51, 2250 (1983).
see, e.g., J. Fröhlich ‘Statistics of fields, the Yang-Baxter equation and the theory of knots and links’, to appear in the proceedings of Cargèse Summer School 1987.
Wu, Y. S., Phys. Rev. Lett. 52, 2106 (1984); 53, 111 (1984).
Laughlin, R. B., Phys. Rev. Lett. 50, 1395 (1983); Halperin, B. I., Phys. Rev. Lett. 52, 1583 (1984); Arovas, D. A., Schrieffer, R., and Wilczek, F., Phys. Rev. Lett. 53, 722 (1984); Tao, R., and Wu, Y. S., Phys. Rev. B31, 6859 (1985); Thouless, D. J., Wu, Y. S., Phys. Rev. B31, 1191 (1985); Arovas, D. A., Schrieffer, R., Wilczek, F., and Zee, A., Nucl. Phys. B251, 117 (1985).
Wiegmann, P. B., Superconductivity in strongly correlated electronic systems and confinement vs. deconfinement phenomena, preprint 1987; Laughlin, R. B., Superconducting ground state of noninteracting particles obeying fractional statistics, preprint 1988.
Fröhlich, J. and Marchetti, P. A., Commun. Math. Phys. 112, 343 (1987); Marchetti, P. A., Europhys. Lett. 4, 663 (1987); Fröhlich, J. and Marchetti, P. A., Bosonization, topological solitons and fractional charges in two-dimensional quantum field theory, Commun. Math. Phys. 116, 127 (1988).
Fröhlich, J. and Marchetti, P. A., Quantum field theories of vortices and anyons, preprint 1988.
Wigner, E., Ann. of Math. 40, 149 (1939); Bargmann, V., Ann. of Math. 48, 568 (1947).
Buchholz, D. and Fredenhagen, K., Commun. Math. Phys. 84, 1 (1982).
Doplicher, S., Haag, R., and Roberts, J. E., Commun. Math. Phys. 13, 1 (1969); 15, 173 (1969); 23, 199 (1971); 35, 49 (1974).
Fröhlich, J. and Marchetti, P. A., Commun. Math. Phys. 112, 343 (1987); Barata, J. C. A., and Fredenhagen, K., Commun. Math. Phys. 113, 403 (1987); Marchetti, P. A., Particle structure analysis of soliton sectors in massive lattice field theories, to appear in Commun. Math. Phys.
Becher, P. and Joos, H., Z. Phys. C15, 343 (1982).
Paul, K. and Khore, A., Phys. Lett. B174, 420 (1986); see also: Deser, S., Jackiw, R., and Templeton, S., Ann. Physics 140, 372 (1982).
Fröhlich, J., Osterwalder, K., and Seiler, E., Ann. of Math. 118, 461 (1981); Seiler, E., Gauge Theories as a Problem in Constructive Quantum Field Theory and Statistical Mechanics, Lecture Notes in Physics Vol. 159, Springer, Berlin, Heidelberg, New York, 1982; see also [6].
see e.g., Isham, C. J., Phys. Lett. B106, 188 (1981).
Brydges, D., Fröhlich, J., and Seiler, E., Ann. Phys. (NY) 121, 227 (1979).
Fröhlich, J., Statistics and monodromy in two-and three dimensional quantum field theory, in K. Bleuler et. al. (eds.). Proc. 1987 Como Conference
Arovas, D. A., Schrieffer, R., Wilczek, F., and Zee, A., Nucl. Phys. B251, [FS13], 117 (1985). (Some additional details have been worked out in: S. Kind, diploma thesis, ETH 1988.)
Polyakov, A. M., Preprint, Landau Institute, 1988.
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Fröhlich, J., Marchetti, PA. Quantum field theory of anyons. Lett Math Phys 16, 347–358 (1988). https://doi.org/10.1007/BF00402043
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DOI: https://doi.org/10.1007/BF00402043