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- W2017456503 abstract "Fractional statistics in one space dimension can be defined in two inequivalent ways: (i) By restricting the wave function for the relative two-body problem to the halfline x ⩾ 0, and imposing the boundary condition ψx = ηψ at x = 0. (ii) By quantizing the sp(1, R) algebra of observables x2 ± p2 and xp + px, and noticing that the irreducible hermitian representations are labelled by a real parameter μ. We show that both these cases can be obtained by a dimensional reduction of a system of anyons in two dimensions. Case one corresponds to restricting the motion of the anyons to a line by a confining potential, and we give η as a function of the statistics parameter θ for two different potentials. The second case corresponds to anyons in a magnetic field restricted to the first Landau level, and we find a linear relationship between μ and θ. We also construct coherent states corresponding to anyons in the lowest Landau level, and calculate the corresponding Berry connection. The statistics phase θ is shown to equal the Berry phase corresponding to an interchange of two anyons, thus generalizing previous results for bosons and fermions." @default.
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- W2017456503 date "1992-10-01" @default.
- W2017456503 modified "2023-09-24" @default.
- W2017456503 title "Dimensional reduction in anyon systems" @default.
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- W2017456503 doi "https://doi.org/10.1016/0550-3213(92)90581-u" @default.
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