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

• Autorzy: Marek Bożejko
• Języki publikacji: EN

Abstrakty

EN

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 $ℱ_{q}(𝓗 )$ acting as
Nx₁ ⊗ ⋯ ⊗ xₙ = nx₁ ⊗ ⋯ ⊗xₙ.
Some applications to combinatorial problems are also given.

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 81S05: Canonical quantization, commutation relations and statistics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 59-67

Daty

wydano

2007

Twórcy

autor

Marek Bożejko

• Instytut Matematyczny, Uniwersytet Wrocławski, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc78-0-4