The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Representations of a local current algebra in nonsimply connected space and the Aharonov–Bohm effect
Abstract
A recent paper established technical conditions for the construction of a class of induced representations of the nonrelativistic current group 𝒮Λ𝒦, where 𝒮 is Schwartz’s space of rapidly decreasing C∞ functions, and 𝒦 is a group of C∞ diffeomorphisms of Rs. Bose and Fermi N-particle systems were recovered as unitarily inequivalent induced representations of the group by lifting the action of 𝒦 on an orbit Δ⊆𝒮′ to its universal covering space δ̃. For s⩾3, δ̃ is the coordinate space for N particles, which is simply connected. In two-dimensional space, however, the coordinate space is multiply connected, implying induced representations other than those describing the usual Bose or Fermi statistics; these are explored in the present paper. Likewise the Aharonov–Bohm effect is described by means of induced representations of the local observables, defined in a nonsimply connected region of Rs. The vector potential plays no role in this description of the Aharonov–Bohm effect.
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Citations
Cites
Rudin, W. (1973) · Cited by 13,740
Significance of Electromagnetic Potentials in the Quantum Theory
Aharonov, Y., & Bohm, D. (1959) · Physical Review · doi:10.1103/physrev.115.485 · Cited by 6,996
The Refractive Index in Electron Optics and the Principles of Dynamics
Ehrenberg, W., & Siday, R. E. (1949) · Proceedings of the Physical Society. Section B · doi:10.1088/0370-1301/62/1/303 · Cited by 624
Proof of the charge superselection rule in local relativistic quantum field theory
Strocchi, F., & Wightman, A. S. (1974) · Journal of Mathematical Physics · doi:10.1063/1.1666601 · Cited by 341
Nonrelativistic Current Algebras as Unitary Representations of Groups
Goldin, G. A. (1971) · Journal of Mathematical Physics · doi:10.1063/1.1665610 · Cited by 97
Self-citationAharonov-Bohm Effect from the "Hydrodynamical" Viewpoint
Casati, G., & Guarneri, I. (1979) · Physical Review Letters · doi:10.1103/physrevlett.42.1579 · Cited by 34
A gauge invariant formulation of quantum electrodynamics using local currents
Menikoff, R., & Sharp, D. H. (1977) · Journal of Mathematical Physics · doi:10.1063/1.523291 · Cited by 27
Self-citation
Cited by
Non-Abelian anyons and topological quantum computation
Nayak, C., Simon, S. H., Stern, A., Freedman, M., & Das Sarma, S. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1083 · Cited by 6,861
Theory of the half-filled Landau level
Halperin, B. I., Lee, P. A., & Read, N. (1993) · Physical Review B · doi:10.1103/physrevb.47.7312 · Cited by 1,739
Jackiw, R. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90448-1 · Cited by 1,111
The quantum effects of electromagnetic fluxes
Olariu, S., & Popescu, I. I. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.339 · Cited by 408
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
Mong, R. S. K., Clarke, D. J., Alicea, J., Lindner, N. H., Fendley, P., Nayak, C., Oreg, Y., Stern, A., Berg, E., Shtengel, K., et al. (2014) · Physical Review X · doi:10.1103/physrevx.4.011036 · Cited by 366
Metadata
- Authors
- Goldin, G. A., Menikoff, R., & Sharp, D. H.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1981-08-01
- Volume
- 22
- Issue
- 8
- Pages
- 1664-1668
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1969376386
- Cited by
- 311
- References
- 7
- FWCI
- 3.19
- Type
- journal article
- Language
- en
- Open access
- closed
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