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

Banach Center Publications (2007)

- Volume: 78, Issue: 1, page 59-67
- ISSN: 0137-6934

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topMarek 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 -

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