ABSTRACT
In this chapter, and chapters 5 and 7, we develop relativistic wave equations for particles of spin 0, spin 1/2, and spin 1, respectively. These wave equations take the form of partial differential equations. We view the wave as the carrier of dynamical observables such as energy, momentum, and angular momentum. These waves carry the dynamical information by propagating according to the wave equations. In principle, the only restriction we know on the form of a wave equation is that it be Lorentz covariant; but Lorentz covariance is not sufficient to completely determine the form of a possible wave equation. We will see that a good description of nature can be achieved by requiring the wave equations for free particles to be linear in the wave functions and their derivatives, be at most second order in the differentials, and be local. This latter requirement means that the state of a particle at a given spacetime point, is completely determined by the wave function and its derivatives evaluated at that particular point, and not on neighbouring points.
