Investigation of Lower Dimensional Field-theoretical and Quantum Mechanical Systems with Broken Parity having Topological Non-perturbative Characteristics

Kumar, Abhinav (2015) Investigation of Lower Dimensional Field-theoretical and Quantum Mechanical Systems with Broken Parity having Topological Non-perturbative Characteristics. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

This thesis deals with systems in lower dimensions that violate discrete local symmetries, e.g., parity (Ƥ) and time-reversal (Ƭ), both at field-theoretical and quantum-mechanical levels. The field-theoretical models concerned here correspond mainly to two space and one time (2+1) dimensional Abelian gauge theories of topological nature, with extensions to the non-Abelian counterpart as a dual to topological gravity theories. In these theories, the topology emerges through a term of Chern-Simons (CS) secondary class, that violates reflection-symmetry in spacetime. The quantum mechanical studies include ƤƬ -symmetric systems, which incorporate real spectra under strict parametric conditions and complex otherwise. The corresponding structure of the vector-space and asymptotic conditions have been analyzed. Additionally, complex extension to such systems and ƤƬ -symmetric non-linear systems are also looked upon.

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