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

Marek Bożejko

Marek Bożejko

Banach Center Publications, Tome 75 (2007), p. 59-67 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we give a construction of operators satisfying q-CCR relations for q > 1: $A (f) A * (g) - A * (g) A (f) = q^{N} ⟨ f, g ⟩ I$ and also q-CAR relations for q < -1: $B (f) B * (g) + B * (g) B (f) = {| q |}^{N} ⟨ f, g ⟩ I$ , where N is the number operator on a suitable Fock space $ℱ_{q} ()$ acting as Nx₁ ⊗ ⋯ ⊗ xₙ = nx₁ ⊗ ⋯ ⊗xₙ. Some applications to combinatorial problems are also given.

Publié le : 2007-01-01

Zbl 1140.46323

EUDML-ID : urn:eudml:doc:282489

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-4,
     author = {Marek Bo\.zejko},
     title = {Remarks on q-CCR relations for |q| > 1},
     journal = {Banach Center Publications},
     volume = {75},
     year = {2007},
     pages = {59-67},
     zbl = {1140.46323},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-4}
}

Marek Bożejko. Remarks on q-CCR relations for |q| > 1. Banach Center Publications, Tome 75 (2007) pp. 59-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-4/