12 research outputs found
Oscillator Quantum Algebra and Deformed su(2) Algebra
A difference operator realization of quantum deformed oscillator algebra
with a Casimir operator freedom is introduced. We show that this
have a nonlinear mapping to the deformed quantum su(2) which was
introduced by Fujikawa et al. We also examine the cyclic representation
obtained by this difference operator realization and the possibility to analyze
a Bloch electron problem by .Comment: 9 pages, Late
A Schwinger term in q-deformed su(2) algebra
An extra term generally appears in the q-deformed algebra for the
deformation parameter , if one combines the
Biedenharn-Macfarlane construction of q-deformed , which is a
generalization of Schwinger's construction of conventional , with the
representation of the q-deformed oscillator algebra which is manifestly free of
negative norm. This extra term introduced by the requirement of positive norm
is analogous to the Schwinger term in current algebra. Implications of this
extra term on the Bloch electron problem analyzed by Wiegmann and Zabrodin are
briefly discussed.Comment: 9 pages. A couple of clarifying comments have been added. This
modified version has been published in Mod. Phys. Lett.
An extended q-deformed su(2) algebra and the Bloch electron problem
It is shown that an extended q-deformed algebra with an extra
(``Schwinger '') term can describe Bloch electrons in a uniform magnetic field
with an additional periodic potential. This is a generalization of the analysis
of Bloch electrons by Wiegmann and Zabrodin. By using a representation theory
of this q-deformed algebra, we obtain functional Bethe ansatz equations whose
solutions should be functions of finite degree. It is also shown that the zero
energy solution is expressed in terms of an Askey Wilson polynomial.Comment: 11 pages, Late
A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
A quantum deformation of the Virasoro algebra is defined. The Kac
determinants at arbitrary levels are conjectured. We construct a bosonic
realization of the quantum deformed Virasoro algebra. Singular vectors are
expressed by the Macdonald symmetric functions. This is proved by constructing
screening currents acting on the bosonic Fock space.Comment: 15 pages, latex fil