The Language of Symmetry: Group Theory and Its Applications to Physics

Author: Yunjae Kim, St. Thomas Aquinas Regional Secondary School, North Vancouver, British Columbia, Canada

Abstract

This article provides an intuitive introduction to the role of symmetry in modern physics. We demonstrate how physical laws are dictated by geometric invariance. Using group theory, we define the algebraic properties of discrete and continuous transformation groups. Then, we apply Noether’s theorem to connect the continuous symmetry of space time to physical conservation laws. Moving to the subatomic scale, we show how local gauge symmetries mathematically necessitate forces, explaining the 𝑆𝑈(3)×𝑆𝑈(2)×𝑈(1) group of the Standard Model. Finally, we explore spontaneous symmetry breaking in condensed matter systems.

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