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

Marek Bożejko. "Remarks on q-CCR relations for |q| > 1." Banach Center Publications 78.1 (2007): 59-67. <http://eudml.org/doc/282489>.

@article{MarekBożejko2007,
abstract = {In this paper we give a construction of operators satisfying q-CCR relations for q > 1: $A(f)A*(g) - A*(g)A(f) = q^\{N\}⟨f,g⟩I$ 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.},
author = {Marek Bożejko},
journal = {Banach Center Publications},
keywords = {-CCR relations; -Hermite polynomials; deformed Fock spaces; generalized Brownian motion; set partition statistic},
language = {eng},
number = {1},
pages = {59-67},
title = {Remarks on q-CCR relations for |q| > 1},
url = {http://eudml.org/doc/282489},
volume = {78},
year = {2007},
}

TY - JOUR
AU - Marek Bożejko
TI - Remarks on q-CCR relations for |q| > 1
JO - Banach Center Publications
PY - 2007
VL - 78
IS - 1
SP - 59
EP - 67
AB - 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.
LA - eng
KW - -CCR relations; -Hermite polynomials; deformed Fock spaces; generalized Brownian motion; set partition statistic
UR - http://eudml.org/doc/282489
ER -