| In this work, we trace the role of symmetry throughout the history of theoretical particle physics, paying particular attention to the role of group theory, the formal mathematics of symmetry. After an analysis of the role of conservation laws and invariance in the theory of general relativity, we move on to Weyl's gauge theory of 1918, which was developed within the context of general relativity as an attempt to unify gravitation and electromagnetism. Weyl was trying to exploit an invariance of scale, and although his theory was experimentally refuted, it provided a formulation of the conservation of charge. After the advent of quantum mechanics, gauge theory was reinterpreted by London as an invariance of the wave-function.; Weyl and Wigner studied group theory in the context of quantum mechanics, but the broadness of its application had yet to be appreciated. Symmetry was soon exploited in the nuclear interactions, however, and we examine the events leading to the discovery of SU(2) of isotopic spin. We analyze how the discovery of strangeness was linked to the generalization of SU(2) to SU(3), and also how it led to a differentiation between the strong interactions, which conserve isotopic spin and strangeness, and the weak interactions, which violate these conservation laws, along with the conservation of parity.; Yang and Mills were impressed with gauge invariance, and in 1954, they took the bold step of imposing it upon the Lagrangian of the strong interactions, forcing the introduction of three new gauge fields. There was a problem, however, because although the short-range of the strong interactions implied that these gauge bosons should be massive, they needed to be massless in order to preserve gauge invariance. In addition, efforts were made to extend Yang-Mills theory to the weak interactions, but they also faced the same zero-mass problem. This problem was finally solved in 1967, when Weinberg and Salam showed how gauge boson masses could be generated using spontaneous symmetry breaking. They based a unification of the electromagnetic and weak interactions upon local gauge invariance, and this principle was soon applied to the strong interactions as well. |
