We study the quantization of the coset space SU(3)/U(1){times}U(1), considered as an example of a compact phase space. We embed this system in the flat space {ital C}{sup 6} endowed with a ...Poisson-bracket structure, then quantize it as a constrained system, finding consistency only for isolated symplectic structures. The space of states for each admissible symplectic structure forms an irreducible representation of SU(3). In this way, we recover in the language of constrained dynamics some of the results of the Borel-Weil-Bott theorem and geometric quantization.
By a classical group we mean one of the groups GLn(R), GLn(C), GLn(H), U(p, q), On(C), O(p, q), SO*(2n), Sp2n(C), Sp2n(R), or Sp(p, q). Let G be a classical group and L its Lie algebra. For each x ∈ ...L we determine the closure of the orbit G · x (for the adjoint action of G on L). The problem is first reduced to the case when x is nilpotent. By using the exponential map we also determine the closures of conjugacy classes of G.
Paraparticles of Infinite Order Hartle, James B.; Stolt, Robert H.; Taylor, John R.
Physical review. D, Particles and fields,
01/1970, Letnik:
2, Številka:
8
Journal Article
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