On the class of possible non-local anyon-like operators and quantum groups

We find a class of non-local operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes anyonic operators defined on a lattice.

[1]  M. Chaichian,et al.  Statistics of q-Oscillators, Quons and Relations to Fractional Statistics , 1993, hep-th/9304111.

[2]  M. R-Monteiro,et al.  Anyonic realization of SUq(N) quantum algebra , 1993, hep-th/9302111.

[3]  A. Lerda,et al.  Anyons and quantum groups , 1993, hep-th/9301100.

[4]  D. Eliezer,et al.  Anyonization of lattice Chern-Simons theory , 1992 .

[5]  Frank Wilczek,et al.  Fractional statistics and anyon superconductivity , 1990 .

[6]  V. Pasquier,et al.  Common structures between finite systems and conformal field theories through quantum groups , 1990 .

[7]  M. Lüscher.  Bosonization in (2+1)-Dimensions , 1989 .

[8]  A. J. Macfarlane,et al.  On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q , 1989 .

[9]  L. C. Biedenharn,et al.  The quantum group SUq(2) and a q-analogue of the boson operators , 1989 .

[10]  E. Fradkin,et al.  Jordan-Wigner transformation for quantum-spin systems in two dimensions and fractional statistics. , 1989, Physical review letters.

[11]  D. Varshalovich,et al.  Quantum Theory of Angular Momentum , 1988 .

[12]  Michio Jimbo,et al.  Aq-difference analogue of U(g) and the Yang-Baxter equation , 1985 .

[13]  K. Menger.  Algebra of Analysis , 1945 .

[14]  E. Wigner,et al.  Über das Paulische Äquivalenzverbot , 1928 .

[15]  A. Lerda.  Anyons: Quantum Mechanics of Particles with Fractional Statistics , 1992 .

[16]  L. Chau,et al.  Differential Geometric Methods in Theoretical Physics , 1990 .

[17]  Takahiro Hayashi,et al.  Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras , 1990 .

[18]  D. Mattis.  Quantum Theory of Angular Momentum , 1981 .

[19]  E. Wigner,et al.  About the Pauli exclusion principle , 1928 .