dc.contributor.author Randriamaro, Hery dc.date.accessioned 2018-06-26T08:45:37Z dc.date.available 2018-06-26T08:45:37Z dc.date.issued 2018-06-25 dc.identifier.uri http://publications.mfo.de/handle/mfo/1368 dc.description.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 $a_{j,l} a_{i,k}^{\dag} = q _{i,k}^{\dag} a_{j,l} + q^{\beta_{-k,l}} \delta_{i,j}$. 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 $\mathtt{cinv}$ en_US and representations of the colored permutation group. dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,11 dc.subject Infinite statistics en_US dc.subject Quon algebra en_US dc.subject Hilbert space en_US dc.subject Colored permutation group en_US dc.title A Deformed Quon Algebra en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-11 local.scientificprogram OWLF 2017 en_US local.series.id OWP-2018-11 en_US local.subject.msc 05 en_US local.subject.msc 81 en_US local.subject.msc 15 en_US
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