Won-Sang Chung

Generalized deformed algebra

In this paper we construct a generalized deformed algebra having the q-deformed Heisenberg-Weyl algebras and Tamm-Dancoff algebra as its special cases. We also show that the algebra is a Hopf algebra. Moreover we obtain a realization of the generalized deformed su(N) algebra in terms of the generalized deformed Heisenberg-Weyl algebra and discuss the deformed harmonic oscillator problem.

Quantum Z3‐graded space

In this paper the quantum Z3‐graded space is discussed and its differential calculus is investigated and the quantum matrices in quantum Z3‐graded space are obtained.

On position and momentum operators in the q oscillator algebra

The aim of this paper is to study the position and momentum operators in q‐deformed oscillator algebras. The natural form of the position operator is Xp=qpN(a++a)qpN, where p is a real number. This operator is an operator representable by a Jacobi matrix. Using the theory of Jacobi matrices, the theory of classical moment problem and the theory of basic hypergeometric functions, it is shown that, depending on values of q and p, Xp can be unbounded symmetric operator [which has the deficiency indices (1,1) and, hence, is not self‐adjoint, but has self‐adjoint extensions], bounded self‐adjoint operator with continuous simple spectrum or self‐adjoint operator of trace class (therefore, with discrete spectrum with zero as the point of accumulation of eigenvalues). The connection of the q‐deformed Heisenberg relation PX−qXP=1 for the position and momentum operators with a q‐deformation of the quantum harmonic oscillator is also considered.

Comment on the solutions of the graded Yang–Baxter equation

In this comment we obtain two types of solutions of the graded Yang–Baxter equation whose symmetry group is GLqs(1‖1).

New deformed boson algebra

In this article the new deformed boson algebra is proposed and the nonlinear shift operator for the algebra is obtained.

Two parameter deformation of Virasoro algebra

In this paper the two parameter deformation of Virasoro algebra is derived. Two parameter deformation of central charge is also obtained. The operator product expansion for (p,q)‐deformed Virasoro algebra is derived.

On the q-Deformed N = 2 SUSY Algebra

In this paper an alternative example of the q·deformed N=2 SUSY algebra is suggested. This algebra is different from the earlier q-deformed versions of SUSY algebra proposed by Parthasarathy et al. and Spiridonov. The q-deformed boson operators and undeformed fermion operators are used in deforming SUSY algebra.

Quantum deformation of superalgebra

In this paper we discuss two types ofq-deformations of superalgebra.

Theory of q-deformed forms. II. q-deformed differential forms and q-deformed Hamilton equation

In this paper we introduce the q-deformed differential forms and quantum-algebra-valued q-deformed forms. We use these to obtain the q-inner derivative and investigate its properties. As a physical application we discuss the q-deformed Hamilton equation.

Theory of q-deformed forms. III. q-deformed Hodge star, inner product, adjoint operator of exterior derivative, and self-dual yang-mills equation

In this paper we introduce the q-deformed Hodge star operator, q-deformed inner product, and q-deformed adjoint of the q-deformed exterior derivative and investigate their properties. Using this mathematical background, we construct the q-deformed self-dual Yang-Mills theory.