A Deformed Quon Algebra

Randriamaro, Hery. "A Deformed Quon Algebra." Communications in Mathematics 27.2 (2019): 103-112. <http://eudml.org/doc/295014>.

@article{Randriamaro2019,
abstract = {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.},
author = {Randriamaro, Hery},
journal = {Communications in Mathematics},
keywords = {Quon Algebra; Infinite Statistics; Hilbert Space; Colored Permutation Group},
language = {eng},
number = {2},
pages = {103-112},
publisher = {University of Ostrava},
title = {A Deformed Quon Algebra},
url = {http://eudml.org/doc/295014},
volume = {27},
year = {2019},
}

TY - JOUR
AU - Randriamaro, Hery
TI - A Deformed Quon Algebra
JO - Communications in Mathematics
PY - 2019
PB - University of Ostrava
VL - 27
IS - 2
SP - 103
EP - 112
AB - 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.
LA - eng
KW - Quon Algebra; Infinite Statistics; Hilbert Space; Colored Permutation Group
UR - http://eudml.org/doc/295014
ER -