Abstract
Abstract This chapter presents a brief introduction to the Dirac equation. This equation lays the foundation for quantum electrodynamics, which describes interaction of electrons and electromagnetic fields at quantum field theory level. The chapter begins with a derivation of the Dirac equation in terms of the Pauli matrices and Dirac spinors, which is followed by a discussion of some of its direct consequences. It next presents a few special solutions of the equation. It then introduces the Dirac equation coupled with gauge field and establishes the Zeeman effect. It will also discuss some nonlinear Dirac equations including the Thirring model, Soler model, and Gross-Neveu model.
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