Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras

Details Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras

1996-05-29

arxiv.org/abs/hep-th/9605204v1

Pramana 45 (1995) 91-139

Physics

High Energy Physics

High Energy Physics - Theory

This is a revised version of the earlier preprint: mp_arc 94-43. Published version

Scientific paper

10.1007/BF02848256

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are : new algebras for infinite statistics, q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ``doubly-infinite'' statistics, many representations of orthostatistics, Hubbard statistics and its variations.

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