Application of the star-product method to the angular momentum quantization

✍ Scribed by Paul Molin

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 379 KB
• Volume: 25
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00406549

✦ Synopsis

We define a .-product on ~]~3 __ {0} 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 ~ * x ~ 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.