6533b7d6fe1ef96bd1266de6
RESEARCH PRODUCT
Application of the star-product method to the angular momentum quantization
Paul Molinsubject
Casimir effectAngular momentumQuantization (physics)Coadjoint representationSquare rootStar productStatistical and Nonlinear PhysicsGeometryAsymptotic expansionMathematical PhysicsEigenvalues and eigenvectorsMathematicsMathematical physicsdescription
We define a *-product on ℝ3 and solve the polarization equation f*C=0 where C is the Casimir of the coadjoint representation of SO(3). We compute the action of SO(3) on the space of solutions. We then examine the case of non-zero eigenvalues of C, in order to find finite-dimensional representations of SO(3). Finally, we compute \(\sqrt C *\sqrt C \) as an asymptotic series of C. This gives an explanation of the use of the star square root of C in a paper by Bayen et al. instead of its natural square root.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-07-01 | Letters in Mathematical Physics |