Separation of noncommutative differential calculus on quantum Minkowski space

Details Separation of noncommutative differential calculus on quantum Minkowski space Separation of noncommutative differential calculus on quantum Minkowski space

2005-06-13

arxiv.org/abs/math/0506249v1

J.Math.Phys. 47 (2006) 023501

Mathematics

Quantum Algebra

33 pages

Scientific paper

10.1063/1.2165793

Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is shown that this problem can be overcome by a separation of variables. We study the action of the universal L-matrix, appearing in the coproduct of partial derivatives, on generators. Powers of he resulting quantum Minkowski algebra valued matrices are calculated. This leads to a nonlinear coordinate transformation which essentially separates the calculus. A compact formula for general derivatives is obtained in form of a chain rule with partial Jackson derivatives. It is applied to the massive quantum Klein-Gordon equation by reducing it to an ordinary q-difference equation. The rest state solution can be expressed in terms of a product of q-exponential functions in the separated variables.

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