UPSI Digital Repository (UDRep)
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UPSI Digital Repository (UDRep)
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| Abstract : Perpustakaan Tuanku Bainun |
| The first part of this work focuses on the canonical group quantization approach applied to non-commutative spaces, namely plane 1R2 and two-torus T2. Canonical group quantization is a quantization approach that adopts the group structure that respects the global symmetries of the phase space as a main ingredient. This is followed by finding its unitary irreduciblere presentations. The use of non commutative space is motivated by the idea of quantum sub structure of space leading to nontrivial modification of the quantization. Extending to noncommuting phase space includes noncommuting momenta that arises naturally in magnetic background as in Landau problem. The approach taken is to modify the symplectic structures corresponding to the noncommutative plane, noncomrnutative phase space and noncommutative torus and obtain their canonical groups. In all cases, the canonical group is found to be central extensions of the Heisenberg group. Next to consider is to generalize the approach to twisted phase spaces where it employs the technique of Drinfeld twist on the Hopf algebra of the system. The result illustrates that a tool from the can deformation quantization be used in canonical group quantization where the deformed Heisenberg group H. is obtained and its representation stays consistent with the discussion in the literature. In these cond part,the two-parameter deformations of quantum group for Heisenberg group and Euclidean group are studied. Both can be achieved through the contraction procedure on SU(2)q,p quantum group. The study also continues to develop (q,p)-extended Heisenberg quantum group from the previous result. As conclusion,itis shown that the extensionsofHeisenberg group arise from quantizing noncommutative plane, noncommutative phase space, noncommutative two-torus, and twisted phase space. The work on two-parameter deformation of quantum group also further shows generalizations of the extension of Heisenberg group. |
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