On extending PQM models to field theory

Ghosh, Arka (2017) On extending PQM models to field theory. Masters thesis, Indian Instittute of Science Education and Research Kolkata.

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Abstract

Polymer quantization offers a background-independent framework, which is a requirement for quantum theories aiming to describe gravity. Current method of Polymer quantization neither preserves the canonical commutators nor offers a suitable form for a annihilation operator, thus violating the requisites for the concept of normal ordering, as well as Wick’s theorem. Wick’s theorem being central to advanced techniques in QFT, the aim of this thesis is to explore avenues that might yield a modification of the extant PQM that ideally agrees well with both these concepts. We have attempted a formal description of PQM using Dirac’s ladder operators that gurantee factorizability. It has been found that this results in a rich operator algebra that can be used to construct several Hermitian as well as non-Hermitian hamiltonians with real spectra. In the present work, all of these candidate hamiltonians and their spectra are studied in some detail, yielding valuable insights into the best possible modification of PQM using this approach.

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