Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of well-defined scalar product is considered. An example of physical effect in system with generalized statistics is also given.

arXiv:math/9806158AIP conference proceedingsJan 1, 19988 citations

International Journal of Theoretical Physics

Remarks on Effect Algebras

W. A. Majewski, Tomasz I. Tylec

Published Dec 15, 2009• 1 citation

Publisher

DOI: 10.1007/s10773-009-0226-4

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arXiv:math/9806158AIP conference proceedingsJan 1, 19988 citations

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings Hamiltonian, based on polynomially deformed su(2), i.e.,

{\mathrm{su}}_{n}(2)

algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of

\mathcal{N}

atoms in a resonator is found to result from collective effects.