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Keywords:
Quon Algebra; Infinite Statistics; Hilbert Space; Colored Permutation Group
Quon Algebra; Infinite Statistics; Hilbert Space; Colored Permutation Group
Summary:
The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators $a_{i,k}$, $(i,k) \in \mathbb {N}^* \times [m]$, on an infinite dimensional vector space satisfying the deformed $q$-mutator relations $a_{j,l} a_{i,k}^{\dag } = q a_{i,k}^{\dag } a_{j,l} + q^{\beta _{k,l}} \delta _{i,j}$. We prove the realizability of our model by showing that, for suitable values of $q$, the vector space generated by the particle states obtained by applying combinations of $a_{i,k}$'s and $a_{i,k}^{\dag }$'s to a vacuum state $|0\rangle $ is a Hilbert space. The proof particularly needs the investigation of the new statistic cinv and representations of the colored permutation group.
References:
[1] Greenberg, O.W.: Example of Infinite Statistics. Physical Review Letters, 64, 7, 1990, 705, DOI 10.1103/PhysRevLett.64.705 | MR 1036450
[2] Greenberg, O.W.: Particles with small Violations of Fermi or Bose Statistics. Physical Review D, 43, 12, 1991, 4111, DOI 10.1103/PhysRevD.43.4111 | MR 1111424
[3] Zagier, D.: Realizability of a Model in Infinite Statistics. Communications in Mathematical Physics, 147, 1, 1992, 199-210, DOI 10.1007/BF02099535 | MR 1171767
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