ABSTRACT
Field theory is the ultimate consequence of the attempts to reconcile the principles of relativistic invariance with those of quantum mechanics. Negative energy states will be interpreted as antiparticles, and once antiparticles are introduced, which can annihilate with particles, particle number is no longer conserved and we likewise lose the notion of position of a particle. This chapter verifies by direct computation that localising the wave function within the light cone will indeed require negative energy states. It discusses the positive square root of the Klein–Gordon equation and solves the Schrodinger equation for the initial condition. As the Schrodinger equation is first order in time, the initial condition uniquely fixes the wave function for all later times, and there will be a unique answer to the question whether the wave function vanishes outside the light cone.
