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dc.contributor.authorRandriamaro, Hery
dc.date.accessioned2018-06-26T08:45:37Z
dc.date.available2018-06-26T08:45:37Z
dc.date.issued2018-06-25
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1368
dc.description.abstractThe 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 $\mathtt{cinv}$ and representations of the colored permutation group.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2018,11
dc.subjectInfinite statisticsen_US
dc.subjectQuon algebraen_US
dc.subjectHilbert spaceen_US
dc.subjectColored permutation groupen_US
dc.titleA Deformed Quon Algebraen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2018-11
local.scientificprogramOWLF 2017en_US
local.series.idOWP-2018-11en_US
local.subject.msc05en_US
local.subject.msc81en_US
local.subject.msc15en_US


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