Abstract
One usually does not think of quantum statistics in terms of a continuous parameter, such as a coupling constant. We are accustomed to the notion that many-particle wave functions are either symmetric or antisymmetric:
where θ = 2nπ for bosons and θ = (2n + 1)π for fermions. Interpolating in θ, e.g., θ = π/2, seems to make no sense because iterating Eq. (1) twice gives
and the single-valuedness of Ψ demands that e^{2i\emptyset }= 1, so one concludes that Bose and Fermi statistics exhaust all the allowed values of θ.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y.-S. Wu, Phys. Rev. Lett. 52, 2103 (1984).
J. M. Leinaas and J. Myrheim, Nuovo Cimento 37B, 1 (1977).
R. MacKenzie and F. Wilczek, Int. J. Mod. Phys. A 3, 2827 (1988).
M. G. G. Laidlaw and C. M. DeWitt, Phys. Rev. D 3, 6 (1971).
Y.-S. Wu, Phys. Rev. Lett. 53, 111 (1984).
F. Wilczek, Phys. Rev. Lett. 48, 1144 (1982).
F. Wilczek, Phys. Rev. Lett. 49, 957 (1982).
I thank S. Kivelson for making this point clear to me.
D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985).
D. P. Arovas, Ph.D. thesis (University of California at Santa Barbara, 1986).
M. D. Johnson and G. S. Canright, Phys. Rev. B 42, 7931 (1990).
D. P. Arovas in Geometric Phases in Physics (A. Shapere and F. Wilczek, eds.), World Scientific, New York, 1989.
S. F. Edwards and Y. V. Gulyaev, Proc. R. Soc. London A279, 229 (1964).
D. Peak and A. Inomata, J. Math. Phys. 10, 1422 (1969).
A. Inomata and V. A. Singh, J. Math. Phys. 19, 12318 (1978); C. C. Gerry and V. A. Singh, Phys. Rev. D 20, 2550 (1979); C. C. Gerry and V. A. Singh, Nuovo Cimento 73B, 161 (1983).
M. D. Johnson and G. S. Canright, Phys. Rev. B 41, 6870 (1990).
M. V. Berry, Proc. R. Soc. London A392, 45 (1984).
B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984).
R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
D. Arovas, J. R. Schrieffer, and F. Wilczek, Phys. Rev. Lett. 53, 722 (1984).
F. D. M. Haldane, unpublished.
S. M. Girvin and Terrence Jach, Phys. Rev. B 29, 5617 (1984).
B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984).
N. Read, unpublished.
R. Tao, J. Phys. C 18, L1003 (1985).
S. M. Girvin in The Quantum Hall Effect (R. Prange and S. M. Girvin, eds.), Springer-Verlag, New York, 1985; S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987).
S. C. Zhang, T. H. Hansson, and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989).
N. Read, Phys. Rev. Lett. 62, 86 (1989).
For a discussion, see A. S. Goldhaber and S. A. Kivelson, Phys. Lett. B 255, 445 (1991).
X.-G. Wen and A. Zee, Phys. Rev. Lett. 62, 1937 (1989).
D.-H. Lee and M. P. A. Fisher, Phys. Rev. Lett. 63, 8 (1989).
D.-H. Lee and C. L. Kane, Phys. Rev. Lett. 64, 1313 (1990).
S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Phys. Rev. Lett. 54, 581 (1985); Phys. Rev. B 33, 2481 (1986).
Daniel P. Arovas, Assa Auerbach, and F. D. M. Haldane, Phys. Rev. Lett. 60, 531 (1988).
S. M. Girvin and D. P. Arovas, Phys. Scr. T27, 156 (1989).
R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); R. B. Laughlin, Science 242, 525 (1988).
A. Fetter, C. Hanna, and R. B. Laughlin, Phys. Rev. B 39, 9679 (1989).
X.-G. Wen, F. Wilczek, and A. Zee, Phys. Rev. B 39, 11,413 (1989).
Y.-H. Chen, F. Wilczek, E. Witten, and B. I. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
D. P. Arovas and F. D. M. Haldane, “Magnetic Band Structure of Ideal Flux Lattices” (in preparation).
J. R. Schrieffer, Theory of Superconductivity, Benjamin-Cummings, New York, 1964.
E. Fradkin, Phys. Rev. B 42, 570 (1990).
S. Deser, R. Jackiw, and S. Templeton, Phys. Rev. Lett. 48, 975 (1982); J. Schonfeld, Nucl. Phys. B185, 157 (1981).
F. Wilczek and A. Zee, Phys. Rev. Lett. 51, 2250 (1983).
Y.-S. Wu and A. Zee, Phys. Lett. 147B, 325 (1984); Nucl. Phys. B272, 322 (1986).
G. Semenoff, Phys. Rev. Lett. 61, 517 (1988). au48._P. Wiegmann, numerous preprints and private communications.
P. Wiegmann, numerous preprints and private communications.
S. M. Girvin, A. H. MacDonald, M. P. A. Fisher, S.-J. Rey, and J. P. Sethna, Phys. Rev. Lett. 65, 1671 (1990).
F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983).
A. H. MacDonald, G. C. Aers, and M. W. C. Dharma-wardana, Phys. Rev. B 31, 5529 (1985).
Georgi E. Shilov, Linear Algebra, Dover, New York, 1977.
S. M. Girvin, Phys. Rev. B 29, 6012 (1984).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Arovas, D.P. (1992). Fractional Statistics in Quantum Mechanics. In: Teitelboim, C., Zanelli, J. (eds) Quantum Mechanics of Fundamental Systems 3. Series of the Centro de Estudios Científicos de Santiago. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3374-0_1
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3374-0_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6489-4
Online ISBN: 978-1-4615-3374-0
eBook Packages: Springer Book Archive