| Title:
|
A Deformed Quon Algebra (English) |
| Author:
|
Randriamaro, Hery |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
27 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
103-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Quon Algebra |
| Keyword:
|
Infinite Statistics |
| Keyword:
|
Hilbert Space |
| Keyword:
|
Colored Permutation Group |
| MSC:
|
05E15 |
| MSC:
|
15A15 |
| MSC:
|
81R10 |
| idZBL:
|
Zbl 1464.05357 |
| idMR:
|
MR4058169 |
| . |
| Date available:
|
2020-02-20T08:59:29Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147985 |
| . |
| Reference:
|
[1] Greenberg, O.W.: Example of Infinite Statistics.Physical Review Letters, 64, 7, 1990, 705, MR 1036450, 10.1103/PhysRevLett.64.705 |
| Reference:
|
[2] Greenberg, O.W.: Particles with small Violations of Fermi or Bose Statistics.Physical Review D, 43, 12, 1991, 4111, MR 1111424, 10.1103/PhysRevD.43.4111 |
| Reference:
|
[3] Zagier, D.: Realizability of a Model in Infinite Statistics.Communications in Mathematical Physics, 147, 1, 1992, 199-210, MR 1171767, 10.1007/BF02099535 |
| . |
