skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Fractional statistics from gravitation

Abstract

We show that the solitons of the SO(3) nonlinear sigma model in 2+1 dimensions, when coupled to gravitation with the gravitational Chern-Simons interaction, become anyons in the absence of the Hopf term. In particular we calculate the fractional statistical factor of the gravitating anyons, and prove that the gravitational Chern-Simons term itself can be interpreted as the Hopf term of the topological current of [Pi][sub 2]([ital S][sup 2]).

Authors:
 [1];  [2]
  1. (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States))
  2. (Center for Theoretical Physics, Seoul National University, Seoul, 151-742 (Korea, Republic of))
Publication Date:
OSTI Identifier:
7116943
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review, D (Particles Fields); (United States); Journal Volume: 49:12
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GRAVITATION; STATISTICAL MECHANICS; SIGMA MODEL; SOLITONS; ANYONS; NONLINEAR PROBLEMS; SO-3 GROUPS; THREE-DIMENSIONAL CALCULATIONS; BOSON-EXCHANGE MODELS; LIE GROUPS; MATHEMATICAL MODELS; MECHANICS; PARTICLE MODELS; PERIPHERAL MODELS; QUASI PARTICLES; SO GROUPS; SYMMETRY GROUPS 662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-); 661310 -- Relativity & Gravitation-- (1992-); 661300 -- Other Aspects of Physical Science-- (1992-)

Citation Formats

Cho, Y.M., and Park, D.H. Fractional statistics from gravitation. United States: N. p., 1994. Web. doi:10.1103/PhysRevD.49.R6269.
Cho, Y.M., & Park, D.H. Fractional statistics from gravitation. United States. doi:10.1103/PhysRevD.49.R6269.
Cho, Y.M., and Park, D.H. 1994. "Fractional statistics from gravitation". United States. doi:10.1103/PhysRevD.49.R6269.
@article{osti_7116943,
title = {Fractional statistics from gravitation},
author = {Cho, Y.M. and Park, D.H.},
abstractNote = {We show that the solitons of the SO(3) nonlinear sigma model in 2+1 dimensions, when coupled to gravitation with the gravitational Chern-Simons interaction, become anyons in the absence of the Hopf term. In particular we calculate the fractional statistical factor of the gravitating anyons, and prove that the gravitational Chern-Simons term itself can be interpreted as the Hopf term of the topological current of [Pi][sub 2]([ital S][sup 2]).},
doi = {10.1103/PhysRevD.49.R6269},
journal = {Physical Review, D (Particles Fields); (United States)},
number = ,
volume = 49:12,
place = {United States},
year = 1994,
month = 6
}
  • The authors suggest that the origin of the odd-denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which govern quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics do not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus, no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references.
  • Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carrymore » fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed.« less
  • The free massless field in 2+1 dimensions is written as an ''integral'' over free massless fields in 1+1 dimensions. Taking the operators with fractional dimension in the Gaussian model as a springboard we construct operators with fractional statistics in the former theory.
  • Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. The authors study the relationship between both theories in 2 + 1 dimensions and the authors show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST-BFV quantization is reviewed in order tomore » understand the topological approach proposed here.« less
  • We show that the particles in the Calogero-Sutherland model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.