A Deformed Quon Algebra
Communications in Mathematics, Tome 27 (2019) no. 2, pp. 103-112
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
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.
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.
Classification :
05E15, 15A15, 81R10
Keywords: Quon Algebra; Infinite Statistics; Hilbert Space; Colored Permutation Group
Keywords: Quon Algebra; Infinite Statistics; Hilbert Space; Colored Permutation Group
@article{COMIM_2019_27_2_a3,
author = {Randriamaro, Hery},
title = {A {Deformed} {Quon} {Algebra}},
journal = {Communications in Mathematics},
pages = {103--112},
year = {2019},
volume = {27},
number = {2},
mrnumber = {4058169},
zbl = {1464.05357},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COMIM_2019_27_2_a3/}
}
Randriamaro, Hery. A Deformed Quon Algebra. Communications in Mathematics, Tome 27 (2019) no. 2, pp. 103-112. http://geodesic.mathdoc.fr/item/COMIM_2019_27_2_a3/
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