Strict deformation quantization ofa particle in external gravitational and Yang — Mills fields

  title={Strict deformation quantization ofa particle in external gravitational and Yang — Mills fields},
  author={Nicolaas P. Landsman},
An adaptationof Rieffel’s notion of “strict deformation quantization” is applied to a particle moving on an arbitrary Riemannianmanifold Q in an externalgaugefield, that is, a connection on a principal H-bundle P over Q. Hence the PoissonalgebraA 0 = C0 ( (T* P)/H) is deformedinto theC*~algebraA = K (L 2(P)~ of H-invariant compact operatorson L2(P), which is is morphicto ~C(L2(Q))®C* (H), involving thegroupalgebra of H. Planck’sconstanth is a genuinenumberratherthan a formal expansionparameter… CONTINUE READING
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