Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation

Details Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation

2003-05-02

arxiv.org/abs/quant-ph/0305012v2

Physics

Quantum Physics

Latex, 54 pages, Section VII enlarged, new references added

Scientific paper

We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically generalised to accommodate new features which arise when the configuration space changes from $n$-dimensional Euclidean space ${\cal R}^n$ to a Lie group $G$. The notion of canonical momentum is carefully analysed, and the meanings of marginal probability distributions and their recovery from the Wigner distribution are clarified. For the case of compact $G$ an explicit definition of the Wigner distribution is proposed, possessing all the required properties. Geodesic curves in $G$ which help introduce a notion of the `mid point' of two group elements play a central role in the construction.

Affiliated with

Also associated with

No associations

Rating

Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation 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 Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-703902