Anyons and Quantum Groups

Abstract

Anyonic oscillators with fractional statistics are built on a two-dimensional square lattice by means of a generalized Jordan-Wigner construction, and their deformed commutation relations are thoroughly discussed. Such anyonic oscillators, which are non-local objects that must not be confused with $q$-oscillators, are then combined à la Schwinger to construct the generators of the quantum group $SU(2{)}_q$ with $q=\exp (\mathrm{i}\pi \nu )$, where $\nu$ is the anyonic statistical parameter.

26 pp., TeX file (figures on request), DFTT 73/92 and ITP-SB-92-73

References in corpus (1)

• Anyonic Realization of $S{U}_q(N)$ Quantum Algebra

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• Quantum groups as hidden symmetries of quantum impurities
• Lagrangian and Hamiltonian Formalism on a Quantum Plane
• Generalized Statistics and Dynamics in Curved Spacetime
• Slave Anyons in the $t$-$J$ Model at the Supersymmetric Point
• Analytical approach to the Bose polaron \\ via $q$-deformed Lie algebra
• $q$-deformed Fermion in Many-Particle Systems and Its Application to BCS Theory
• Intermediate statistics: addressing the thermoelectric properties of solids
• $q$-Deformed Classical Lie Algebras and their Anyonic Realization
• On the R-Matrix Formulation of Deformed Algebras and Generalized Jordan-Wigner Transformations
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• Generalized partition functions and interpolating statistics
• Structure of Multi-Anyon Wavefunctions
• Gauge-invriant quasi-free states on the algebra of the anyon commutation relations
• Anyonic quasiparticles of hardcore anyons
• Fractal von Neumann entropy
• Thermodynamics of Statistical Anyons
• Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)})
• Translation-Invariant Noncommutative Gauge Theories, Matrix Modeling and Noncommutative Geometry
• Intermediate statistics: addressing the Landau diamagnetism problem
• Finite Temperature Behaviors of q-deformed Fermi Gases
• Quasi-Continuous Symmetries of Non-Lie Type
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• q-deformed conformal correlation functions
• Quantum Gauge Theories
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• Measuring Chern-Simons level $k$ by braiding $SU(2{)}_k$ anyons
• Deformed $C_{\lambda }$-Extended Heisenberg Algebra in Non-commutative Phase-Space
• Exotic Particles and $w_{\infty }$-Algebras in Two- and High-Dimensional Spaces