In the previous chapter, we have seen that the nonrelativistic equation of motion of a free particle can be generalized in a natural way to the relativistic regime by making homogeneous its dependence on space and time. There are two possibilities. The first, involving second-order derivatives and called the Klein—Gordon equation, governs the evolution of fields of integral spins which are associated with operators that obey commutation relations. The second, containing only first-order derivatives and discovered by P. A. M. Dirac in 1928 in his search for a relativistic formalism admitting a non-negative probability density, describes the dynamics of fields having spins ½. These fields must then represent particles, such as the electron, the proton, or the quarks, that constitute the bulk of visible matter in the universe. They are the subject of the present chapter.
KeywordsDirac Equation Lorentz Transformation Dirac Particle Dirac Spinor Weyl Spinor
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