Physics – Mathematical Physics
Scientific paper
2007-01-05
J. Phys. A: Math. Theor. 40 (2007) 3869-3888
Physics
Mathematical Physics
Scientific paper
In a Wigner quantum mechanical model, with a solution in terms of the Lie superalgebra gl(1|n), one is faced with determining the eigenvalues and eigenvectors for an arbitrary self-adjoint odd element of gl(1|n) in any unitary irreducible representation W. We show that the eigenvalue problem can be solved by the decomposition of W with respect to the branching gl(1|n) --> gl(1|1) + gl(n-1). The eigenvector problem is much harder, since the Gel'fand-Zetlin basis of W is involved, and the explicit actions of gl(1|n) generators on this basis are fairly complicated. Using properties of the Gel'fand-Zetlin basis, we manage to present a solution for this problem as well. Our solution is illustrated for two special classes of unitary gl(1|n) representations: the so-called Fock representations and the ladder representations.
der Jeugt Joris Van
Lievens S.
Stoilova Neli I.
No associations
LandOfFree
On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications 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 On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-16488