Physics – Mathematical Physics
Scientific paper
2011-11-03
J. Math. Phys. 52 (2011), 113503 (21 pp)
Physics
Mathematical Physics
Scientific paper
10.1063/1.3659286
In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and the Heisenberg equations are the starting point, and no further assumptions are made about how the position and momentum operators commute. Wigner quantization leads to new classes of solutions, and representations of Lie superalgebras are needed to describe them. For the n-dimensional Wigner harmonic oscillator, solutions are known in terms of the Lie superalgebras osp(1|2n) and gl(1|n). For n=3N, the question arises as to how the angular momentum decomposition of representations of these Lie superalgebras is computed. We construct generating functions for the angular momentum decomposition of specific series of representations of osp(1|6N) and gl(1|3N), with N=1 and N=2. This problem can be completely solved for N=1. However, for N=2 only some classes of representations allow executable computations
der Jeugt Joris Van
Regniers Gilles
No associations
LandOfFree
Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator 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 Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-701528