On commutation relations for quons

Abstract

The model of generalized quons is described in a purely algebraic way. Commutation relations and corresponding consistency conditions for our generalized quons system are studied in terms of quantum Weyl algebras. Fock space representation and corresponding scalar product is also given. *

OnC*-algebras generated by pairs ofq-commuting isometries

“…The limiting cases q = −1 and q = 1 correspond to algebras of the CCRs and the CARs, and the question was raised in [6] whether the C * -algebras E q are in fact isomorphic for all q in the "natural" interval, −1 < q < 1. This has since become a conjecture of some standing, see, e.g., [10]. We show that there is a closely related deformation family, and we resolve the question for this deformation in the affirmative, in the case n = 2.…”

“…A special case of (1) is the case of the algebras generated by q-commuting isometries. It was shown in [13] that the C * -algebras generated by the generalized quonic relations, see [10], can be generated by isometries satisfying relations of the form…”

Deformed Exterior Algebra, Quons and their Coherent States

“…So these relations arise in a natural way, instead of being imposed to obtain the socalled generalized quons [Marcinek (1998)]. Now, and by referring to the classical limit (q = 1or q = −1), we will give the statistical properties of the quons Algebra (68).…”

Quantum-classical interactions and galois type extensions

“…We assume that every charge is equipped with the ability to absorb and emit quanta of a certain nature. A system that contains a charge and a certain number of quanta as a result of interaction with the quantum environment is said to be a dressed particle [16,18]. A particle dressed with a single quantum is a fictitious particle called a quasi-particle.…”