Abstract:

The artists of the Renaissance said that man’s main concern should be for man, and yet there are other things of interest in the world. Even the artists appreciate sunsets, ocean waves, and the march of the stars across the heavens. There is then some reason to talk of other things sometimes. As we look into these things, we directly get aesthetic pleasure from them on observation. There is also a rhythm and a pattern between the phenomena of nature which is not apparent to the eye, but only to the eye of analysis; and it is these rhythms and patterns which we call Physical Laws.” (Richard P. Feynman)

The ability of science to combine seemingly unrelated phenomena is exceptional. Yet, great minds have been trying to connect different natural processes in one mathematical framework for a long time. The patterns extracted from intuitive phenomena have been generalized with the help of non-intuitive abstract mathematics. We, human beings, then rewire our brains, and oddly, we have built with the capacity of rewiring. It is not hard to tell that Albert Einstein was the first who knowingly or unknowingly developed the general framework for Gauge Theories. But later, he got out of the picture because of his resilience against Quantum Mechanics. The next era of geniuses developed the Standard Model of Particles by following Einstein’s theoretical formalism. But the madness did not stop there, and they went further by forming more generalized patterns. ‘The generalized patterns’ are the theme of my thesis. This study aims to explain the general mathematical machinery used to develop any Gauge Theory. It touches Group Theory and The Standard Model to take you out of abstraction to the Physics World. In the end, it rigorously explains the ‘Beyond Standard Model’ segment. It discusses the Gauge groups SU(5) and SO(10) and external symmetries augmented with Grassman Variables, which lead to Supersymmetric Theories (SUSY). The thesis is a journey to develop complicated concepts by generalizing the intuitively understandable patterns.