Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9304103 · Modern Physics Letters A

THREE-LOOP CALCULATION OF THE ANYONIC FULL CLUSTER EXPANSION

Roberto Emparan, M.A. VALLE BASAGOITI

Published Nov 10, 1993• 15 citations
arXivHTMLPDF

Abstract

We calculate the perturbative correction to every cluster coefficient of a gas of anyons through second order in the anyon coupling constant, as described by Chern-Simons field theory.
DOI
10.1142/s0217732393002221

Related papers

Pressure in Chern-Simons field theory to three-loop order

M.A. Valle Basagoiti

arXiv:hep-th/9305011•Physics Letters B•Jun 1, 1993•18 citations

Perturbative equation of state for a gas of anyons Second order

Alain Dasnières de Veigy, Stéphane Ouvry

Physics Letters B•Sep 1, 1992•30 citations

Many-Body Methods for Chern-Simons Systems

Lucjan Jacak, Piotr Sitko, Konrad Wieczorek +1 more

This chapter addresses the quantum theory of many-body systems with Chern–Simons field in order to describe the change of statistics in two-dimensional systems. The random phase approximation is used for an anyon gas. Within this approach the correlation energy of an anyon gas is found. The Hartree–Fock approximation for Chern–Simons systems and diagram analysis for a gas of anyons for self-consistent Hartree and Hartree–Fock approximations is also given.

Oxford University Press eBooks•Sep 25, 2003•0 citations

Fractional Quantum Hall Effect and Topological Order: Wavefunctions, Anyons, and Chern-Simons Field Theory

Abednour Laidi

Master's thesis in Theoretical Physics. The official university title is "Fractional Quantum Hall Effect: Current State and Perspectives"; this record uses the author's preferred, more descriptive title. This thesis develops a unified description of the fractional quantum Hall effect (FQHE) and topological order through three complementary frameworks: microscopic trial many-body wavefunctions, the algebraic theory of anyons and unitary modular tensor categories, and Chern-Simons effective field theory. The first part covers the physical foundations—Landau quantization, the TKNN invariant, Laughlin's wavefunctions, the hierarchy and composite fermion theories, and some non-Abelian states like the Moore-Read Pfaffian state. The second part develops the algebraic theory of anyons, from the braid group to fusion rules, quantum dimensions, topological spins, and the F- and R-matrices that characterize a unitary modular tensor category. The third part constructs the Chern-Simons effective field theory, deriving fractional charge, statistics, and ground-state degeneracy, unifying Abelian states via the K-matrix formalism, and then generalizing to non-Abelian states through 𝑈(1)ₘ × 𝑆𝑈(𝑁)ₖ Chern-Simons theory. The central result is that Chern–Simons theory provides a field-theoretic realization of the topological order introduced microscopically and algebraically in the earlier chapters, closing the circle between the three descriptions and providing a unified framework for the FQHE and topological order and anyon's physics.

•Oct 12, 2026•0 citations

Perturbative equation of state for a gas of anyons

Alain Comtet, John McCabe, Stéphane Ouvry

Physics Letters B•May 1, 1991•59 citations

Fractional exclusion statistics and anyons

Wei Chen, Yee Jack Ng

Do anyons, dynamically realized by the field theoretic Chern-Simons construction, obey fractional exclusion statistics? We find that they do if the statistical interaction between anyons and antianyons is taken into account. For this anyon model, we show perturbatively that the exchange statistical parameter of anyons is equal to the exclusion statistical parameter. We obtain the same result by applying the relation between the exclusion statistical parameter and the second virial coefficient in the nonrelativistic limit.

arXiv:cond-mat/9411008•Physical review. B, Condensed matter•May 15, 1995•6 citations
Master's thesis in Theoretical Physics. The official university title is "Fractional Quantum Hall Effect: Current State and Perspectives"; this record uses the author's preferred, more descriptive title. This thesis develops a unified description of the fractional quantum Hall effect (FQHE) and topological order through three complementary frameworks: microscopic trial many-body wavefunctions, the algebraic theory of anyons and unitary modular tensor categories, and Chern-Simons effective field theory. The first part covers the physical foundations—Landau quantization, the TKNN invariant, Laughlin's wavefunctions, the hierarchy and composite fermion theories, and some non-Abelian states like the Moore-Read Pfaffian state. The second part develops the algebraic theory of anyons, from the braid group to fusion rules, quantum dimensions, topological spins, and the F- and R-matrices that characterize a unitary modular tensor category. The third part constructs the Chern-Simons effective field theory, deriving fractional charge, statistics, and ground-state degeneracy, unifying Abelian states via the K-matrix formalism, and then generalizing to non-Abelian states through 𝑈(1)ₘ × 𝑆𝑈(𝑁)ₖ Chern-Simons theory. The central result is that Chern–Simons theory provides a field-theoretic realization of the topological order introduced microscopically and algebraically in the earlier chapters, closing the circle between the three descriptions and providing a unified framework for the FQHE and topological order and anyon's physics.
Do anyons, dynamically realized by the field theoretic Chern-Simons construction, obey fractional exclusion statistics? We find that they do if the statistical interaction between anyons and antianyons is taken into account. For this anyon model, we show perturbatively that the exchange statistical parameter of anyons is equal to the exclusion statistical parameter. We obtain the same result by applying the relation between the exclusion statistical parameter and the second virial coefficient in the nonrelativistic limit.