Spin Representations of the q-Poincare Algebra

Details Spin Representations of the q-Poincare Algebra Spin Representations of the q-Poincare Algebra

2001-10-19

arxiv.org/abs/math/0110219v1

Mathematics

Quantum Algebra

Submitted as Ph.D. Thesis on March 8, 2001. Ph.D thesis, Ludwig-Maximilians-Universitaet Muenchen, 2001

Scientific paper

The spin of particles on a non-commutative geometry is investigated within the framework of the representation theory of the q-deformed Poincare algebra. An overview of the q-Lorentz algebra is given, including its representation theory with explicit formulas for the q-Clebsch-Gordan coefficients. The vectorial form of the q-Lorentz algebra (Wess), the quantum double form (Woronowicz), and the dual of the q-Lorentz group (Majid) are shown to be essentially isomorphic. The construction of q-Minkowski space and the q-Poincare algebra is reviewed. The q-Euclidean sub-algebra, generated by rotations and translations, is studied in detail. The results allow for the construction of the q-Pauli-Lubanski vector, which, in turn, is used to determine the q-spin Casimir and the q-little algebras for both the massive and the massless case. Irreducible spin representations of the q-Poincare algebra are constructed in an angular momentum basis, accessible to physical interpretation. It is shown how representations can be constructed, alternatively, by the method of induction. Reducible representations by q-Lorentz spinor wave functions are considered. Wave equations on these spaces are found, demanding that the spaces of solutions reproduce the irreducible representations. As generic examples the q-Dirac equation and the q-Maxwell equations are computed explicitly and their uniqueness is shown.

Affiliated with

Also associated with

No associations

Rating

Spin Representations of the q-Poincare Algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spin Representations of the q-Poincare Algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spin Representations of the q-Poincare Algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-212444