A+ CATEGORY SCIENTIFIC UNIT

Remarks on $q$-CCR relations for $|q|>1$

Volume 78 / 2007

Marek Bo/zejko Banach Center Publications 78 (2007), 59-67 MSC: Primary 46L53; Secondary 81S05. DOI: 10.4064/bc78-0-4

Abstract

In this paper we give a construction of operators satisfying $q$-CCR relations for $q>1$: $$ A(f) A^{*}(g) - A^{*}(g) A(f) = q^{N} \langle f, g \rangle I $$ and also $q$-CAR relations for $q<-1$: $$ B(f) B^{*}(g) + B^{*}(g) B(f) = |q|^{N} \langle f, g \rangle I, $$ where $N$ is the number operator on a suitable Fock space $\mathcal{F}_{q}({\mathcal{H}})$ acting as $$ N x_1\otimes\cdots\otimes x_n = n\, x_1\otimes\cdots\otimes x_n.$$ Some applications to combinatorial problems are also given.

Authors

  • Marek Bo/zejkoInstytut Matematyczny
    Uniwersytet Wroc/lawski
    Plac Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image