# Do anyons solve Heisenberg's Urgleichung in one dimension

@article{Ilieva1998DoAS, title={Do anyons solve Heisenberg's Urgleichung in one dimension}, author={Nevena Ilieva and Walter Thirring}, journal={The European Physical Journal C - Particles and Fields}, year={1998}, volume={6}, pages={705-714} }

Abstract. We construct solutions to the chiral Thirring model in the framework of algebraic quantum field theory. We find that for all positive temperatures there are fermionic solutions only if the coupling constant is $\lambda = \sqrt{2(2n+1)\pi}, \, n\in \bf N$.

## 15 Citations

### Dualities for anyons

- Physics
- 2010

We show that the low-energy dynamics of anyons in (1+1) dimensions with the smallest number of derivatives and , and symmetric interactions are dual to the sine-Gordon model for bosonic fields. We…

### HIERARCHY OF QUANTUM EXPLICITLY SOLVABLE AND INTEGRABLE MODELS

- Physics
- 2006

Realizing bosonic field v(x) as current of massless (chiral) fermions we derive hierarchy of quantum polynomial interactions of the field v(x) that are completely integrable and lead to linear…

### Two-dimensional anyons and the temperature dependence of commutator anomalies

- Physics
- 2001

The temperature dependence of commutator anomalies is discussed on the explicit example of particular (anyonic) field operators in two dimensions. The correlation functions obtained show that effects…

### Off-diagonal correlations in one-dimensional anyonic models: a replica approach

- Mathematics
- 2009

We propose a generalization of the replica trick that allows us to calculate the large distance asymptotics of off-diagonal correlation functions in anyonic models with a proper factorizable…

### One-dimensional impenetrable anyons in thermal equilibrium: I. Anyonic generalization of Lenard's formula

- Physics
- 2008

We have obtained an expansion of the reduced density matrices (or, equivalently, correlation functions of the fields) of impenetrable one-dimensional anyons in terms of the reduced density matrices…

### Correlation functions of one-dimensional Lieb–Liniger anyons

- Physics
- 2007

We have investigated the properties of a model of 1D anyons interacting through a δ-function repulsive potential. The structure of the quasi-periodic boundary conditions for the anyonic field…

### One-dimensional impenetrable anyons in thermal equilibrium: IV. Large time and distance asymptotic behavior of the correlation functions

- Physics
- 2010

This work presents the derivation of the large time and distance asymptotic behavior of the field–field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the…

### Boson-fermion correspondence and quantum integrable and dispersionless models

- Physics
- 2003

This paper is devoted to a detailed description of the notion of boson-fermion correspondence introduced by Coleman and Mandelstam and to applications of this correspondence to integrable and related…

### Nonequilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature

- Physics
- 2020

We derive an exact description of the non-equilibrium dynamics at finite temperature for the anyonic Tonks-Girardeau gas extending the results of Atas et al. [Phys. Rev. A 95, 043622 (2017)] to the…

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