 9443 A.K.Mishra and G.Rajasekaran
 Generalized Fock spaces, new forms of quantum statistics and
their algebras
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Mar 4, 94

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Abstract. We formulate a theory of generalized Fock spaces which underlies the
different forms of quantum statistics such as ``infinite'', BoseEinstein
and FermiDirac statistics. Singleindexed systems as well as
multiindexed systems that cannot be mapped into singleindexed systems
are studied. Our theory is based on a threetiered 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, qstatistics and its many avatars, a consistent
algebra for fractional statistics, null statistics or statistics of
frozen order, ``doublyinfinite'' statistics, many representations of
orthostatistics, Hubbard statistics and its variations.
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