Spin Representations of the q-Poincare Algebra
| dc.creator | Blohmann, Christian | |
| dc.date | 2001-10-19 | |
| dc.date.accessioned | 2026-07-07T04:43:58Z | |
| dc.date.available | 2026-07-07T04:43:58Z | |
| dc.description | 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. | |
| dc.description | Submitted as Ph.D. Thesis on March 8, 2001. Ph.D thesis, Ludwig-Maximilians-Universitaet Muenchen, 2001 | |
| dc.identifier | https://arxiv.org/abs/math/0110219 | |
| dc.identifier | http://arxiv.org/abs/math/0110219 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62450 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | 20G42; 81R60 | |
| dc.title | Spin Representations of the q-Poincare Algebra | |
| dc.type | text |