Separation of noncommutative differential calculus on quantum Minkowski space
- Arnold Sommerfeld Center for Theoretical Physics, Fakultaet fuer Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Munich (Germany)
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 the 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.
- OSTI ID:
- 20768728
- Journal Information:
- Journal of Mathematical Physics, Vol. 47, Issue 2; Other Information: DOI: 10.1063/1.2165793; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras
Relativistic kinetic momentum operators, half-rapidities and noncommutative differential calculus