Aspects of Divergences in Quantum Field Theory and its Relation with Quantum Gravity Phenomenology

Barman, Subhajit (2014) Aspects of Divergences in Quantum Field Theory and its Relation with Quantum Gravity Phenomenology. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Subhajit Barman) Subhajit_Barman-12IP007.pdf - Submitted Version Restricted to Repository staff only Download (480kB)

Abstract

This thesis is divided into 4-main chapters. In the first chapter we have discussed the overview and motivation of our work. In the second chapter an elaborated discussion of regularization and renormalization of λΦ⁴ theory is presented. In this chapter we have considered the regularization and renormalization by the method of cut-off and dimensional regularization. In third chapter a brief overview of polymer quantization is discussed and with this polymer quantization how to find out the simple harmonic oscillator spectra, is also presented. In this third chapter we have also calculated the propagator using the harmonic oscillator spectra derived from the polymer quantization. As a whole we have studied different aspects of divergences coming in λΦ⁴ theory and learned how to mathematically handle those divergences. We have tried to understand the physical reasoning underlying these divergences using polymer quantum mechanics. We have summarized our work and discussed about our future work in the fourth chapter. As a part of our future work we are aiming to study the behavior of the loop corrections, while the corresponding propagator is given by the polymer quantization.

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