Comments on the Hopf Lagrangian and Fractional Statistics of Solitons

Wu, Yong-Shi; Zee, A.

doi:10.1016/0370-2693(84)90126-6

Comments on the Hopf Lagrangian and Fractional Statistics of Solitons

Jul, 1984

5 pages

Published in:

Phys.Lett.B 147 (1984) 325-329

Published: 1984

DOI:

10.1016/0370-2693(84)90126-6

Report number:

DOE-ER-40048-18 P4

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Abstract: (Elsevier)

We show that the nonlocal Hopf lagrangian in a model for solitons obeying fractional statistics, namely the (2 + 1)-dimensional O(3) nonlinear σ-model, can be written in a local form and is locally a total divergence. With these properties the effects of this lagrangian are converted to a multi-valued phase of the wave functional. In doing so we make it clear why an arbitrary nontopological or nonlocal lagrangian does not determine statistics at all.

FIELD THEORETICAL MODEL: SIGMA
FIELD THEORY: NONLINEAR
FIELD THEORY: THREE-DIMENSIONAL
FIELD THEORY: O(3)
FIELD THEORY: SCALAR
FIELD THEORY: EUCLIDEAN
FIELD EQUATIONS: SOLITON
FIELD EQUATIONS: NONLOCAL
FERMION: STATISTICS
WAVE FUNCTION

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