ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Uq(sl(2)) covariant Bose and Fermi oscillators are studied systematically and applied to constructing vertex operators and Uq invariant blocks. For qp=−1 (p=2,3,...) a p2-dimensional unitary Fock space representation of the Bose oscillator algebra A−(q) is constructed. This representation does not allow, however, for the construction of all Uq invariant blocks associated with an indecomposable representation of Uq. An extension of A− is needed in this case, which involves operators creating states of q spin projection ±p/2 from the Fock vacuum. The extended algebra only has infinite-dimensional indefinite metric space representations. An algebraic notion of trace is introduced (provided q2≠1 in the Bose case). This allows the introduction of a family of (in general, mixed) Uq invariant "temperature'' states, such that the vacuum expectation value appears in the zero temperature limit.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529713
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