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Canonical group quantization on non-cotangent bundle phase space and its application in quantum information theory


Citation

Ahmad Sumadi, Ahmad Hazazi (2024) Canonical group quantization on non-cotangent bundle phase space and its application in quantum information theory. Doctoral thesis, Universiti Putra Malaysia.

Abstract

Spin quantization has always been an interesting intrinsic feature in quantum mechanics. This thesis discussed the holomorphic polarization method, motivated by geometric quantization, in a new formulation of canonical group quantization on noncotangent bundle phase space to produce spin quantization. The first part focuses on determining the one-dimensional complex projective space CP1 as a compact phase space and a special unitary group of degree two SU(2) as its canonical group that is not in the semi-direct product form. The emergence of the hidden discrete symmetry which is not deducible from the Lie algebraic structure of SU(2) indicates that it is the double-covering group. Thus its global structure is determined through the lifting SU(2) action on the fibre bundle over phase space. The second part focuses on the quantization process with the holomorphic wavefunction determined through the holomorphic local section of the fibre bundle and the natural polarization arises through the unitary irreducible representation of SU(2) that does not follow Mackey’s induced representation theory. From the representation operators, a set of spin angular momentum operators is generated as complex differential operators associated with a connection-type term l from action on holomorphic wavefunctions. Such representation operators’ matrix elements and characters are determined as Jacobi polynomials and its application in describing the single-qubit pure state is discussed. In conclusion, it is shown that the holomorphic polarization naturally emerged in the canonical group quantization on non-cotangent bundle phase space and has its application in quantum information theory which arises geometrically from the quantization problem.


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Official URL or Download Paper: http://ethesis.upm.edu.my/id/eprint/18372

Additional Metadata

Item Type: Thesis (Doctoral)
Subject: Quantization (Physics)
Subject: Quantum information theory
Subject: Electronic books
Call Number: IPM 2024 1
Chairman Supervisor: Nurisya binti Mohd Shah, PhD
Divisions: Institute for Mathematical Research
Keywords: Canonical group quantization, holomorphic wavefunction, non-cotangent bundle, qubit, spin quantization.
Depositing User: Ms. Rohana Alias
Date Deposited: 04 Aug 2025 06:18
Last Modified: 04 Aug 2025 06:18
URI: http://psasir.upm.edu.my/id/eprint/118371
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