Classically Scale Invariant Models and Automation of Calculations in QFT

Pal, Kuntal (2017) Classically Scale Invariant Models and Automation of Calculations in QFT. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Kuntal Pal (12MS098)) 12MS098.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

The thesis explores two completely different directions. For the first problem, we look into dynamical mass generation through the Coleman Weinberg (CW) mechanism by starting from a theory with no inbuilt mass parameter. Excluding the mass term ensures scale invariance which in turn can help to avoid the quadratic divergences in the mass of the Higgs and hence provide a solution for the problem of fine-tuning cancellation at all orders in perturbation theory. The CW mechanism is first applied to simple models with some modifications in the calculations already available in the literature. Since this idea of spontaneous symmetry breaking fails to generate sufficiently high mass for the Higgs, we try to implement the mechanism with two charged scalars where the vacuum expectation value for one field acts as a mass scale for the other on account of a cross term between the two fields in the potential. In the second problem, we started a journey towards the goal of developing a complete package for the automation of calculations in Quantum Field Theory using the Sympy library in python. We implement symbolic generation of Lagrangian for scalars and fermions along with taking functional derivatives with respect to the fields.

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