Date

5-2-2023

Document Type

Thesis

Abstract

Motivated by the goal of participating in astroparticle physics research in graduate school, we aimed to understand the Standard Model of particle physics and the Feynman diagrams through which particle interactions are described, so that we could learn about the properties of certain astroparticles. The axiomatic principle that governs fundamental physics is manifest covariance, implying that the mathematical forms of the physical laws are the same to all observers. Maintaining covariance requires 4-vector representation using group theoretical techniques based on symmetries, as well as a transition from single-particle quantum physics to many-particle quantum field theory (QFT). The Standard Model of particle physics (SM) accounts for all known particles and three of the four known forces. In this project, we first examined the Standard Model using group theory to preserve covariance. This approach led to particle and force content of the SM. Second, we explored the Standard Model manifestly using quantum field theory and 4-vectors. Going from 1st to 2nd quantization of field theory made it possible to study indistinguishable n-many particles while preserving Special Relativity. Using quantum field theory, we built operator valued relativistic fields where particles were seen as local excitations of the relevant quantum field. We then defined Feynman propagators which represented impulses that we later described as particles. LSZ reduction and Wick’s contractions, together with the Feynman propagators, allowed us to trace up to second-order particle interactions using Feynman diagrams. We followed the canonical approach to QFT in our exploration. Once we built a working understanding of the SM and QFT, we were able to briefly investigate exotic particles such as axions using their Feynman diagrams.

Department

Physics, Photonics, and Optical Engineering

Thesis Comittee

Dr. Edward Deveney, Thesis Advisor
Dr. Thomas P. Kling, Thesis Advisor
Dr. Jeffrey J. Williams, Committee Member

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