Symmetry and the Evolution of Physics

Abstract

This chapter provides an insight into the role of symmetry in the elucidation of the current theories of particle physics. Most of conventional matter of the universe is made up of quarks, leptons, and the gauge and Higgs bosons. Of the four known forces of nature, comprising the strong and weak nuclear forces, the electromagnetic force, and the gravitational force, the first three can be described by quantum field theories (QFTs), each of which has a gauge symmetry represented by a symmetry group. These are U(1) for the electromagnetic, SU(1) for the weak, and SU(2) for the strong force. The Standard Model of particle physics has the SU(2) × SU(1) × U(1) symmetry group. Symmetries may be divided into space–time and internal symmetries, leading to the conservation of extrinsic and intrinsic properties (respectively) of the particles, according to Noether's Theorem. New particles/gauge bosons are discovered theoretically by the gauging principle, where the broken symmetry of the Hamiltonian or Lagrangian is fixed by the introduction of a new component of the force. Theory is related to the experimental scattering cross-section data by guessing at the symmetry being followed, and using relativistic quantum mechanics to calculate the corresponding scattering cross-sections.