Abstract
Abstract This chapter starts with a brief summary of special relativity, describing how 4-vectors and the Lorentz transformation can be represented by complex matrices. Spinors are introduced as basic building blocks of special relativity, allowing a demonstration of how the Weyl equation and the Dirac equation emerge from the Lorentz transformation of spinors. The Klein–Gordon equation is discussed to show the problems and applicability of relativistic quantum mechanics. The Dirac equation for a free particle is then discussed, including the use of different representations (including the Dirac and Weyl representations), discrete symmetries, and the non-relativistic limit. Interactions with the classical electromagnetic field are introduced, demanding a corresponding gauge symmetry. The chapter concludes by extending the gauge symmetry to account for weak and strong interactions.
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