Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-10-02
J.Phys.A36:11999-12019,2003
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, to be published in J.Phys. A
Scientific paper
10.1088/0305-4470/36/48/007
An n-particle 3-dimensional Wigner quantum oscillator model is constructed explicitly. It is non-canonical in that the usual coordinate and linear momentum commutation relations are abandoned in favour of Wigner's suggestion that Hamilton's equations and the Heisenberg equations are identical as operator equations. The construction is based on the use of Fock states corresponding to a family of irreducible representations of the Lie superalgebra sl(1|3n) indexed by an A-superstatistics parameter p. These representations are typical for p\geq 3n but atypical for p<3n. The branching rules for the restriction from sl(1|3n) to gl(1) \oplus so(3) \oplus sl(n) are used to enumerate energy and angular momentum eigenstates. These are constructed explicitly and tabulated for n\leq 2. It is shown that measurements of the coordinates of the individual particles gives rise to a set of discrete values defining nests in the 3-dimensional configuration space. The fact that the underlying geometry is non-commutative is shown to have a significant impact on measurements of particle separation. In the atypical case, exclusion phenomena are identified that are entirely due to the effect of A-superstatistics. The energy spectrum and associated degeneracies are calculated for an infinite-dimensional realisation of the Wigner quantum oscillator model obtained by summing over all p. The results are compared with those applying to the analogous canonical quantum oscillator.
der Jeugt Joris Van
King Ronald C.
Palev Tchavdar D.
Stoilova Neli I.
No associations
LandOfFree
A non-commutative n-particle 3D Wigner quantum 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 A non-commutative n-particle 3D Wigner quantum oscillator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A non-commutative n-particle 3D Wigner quantum oscillator will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-212007