19: Path Integrals for Relativistic Particle Orbits

Particles moving at large velocities near the speed of light are called relativistic particles. If such particles interact with each other or with an external potential, they exhibit quantum effects which cannot be described by their orbital fluctuations alone. At very short interaction times, additional particles or pairs of particles and antiparticles are created or annihilated, and the total number of particle orbits is no longer invariant. Ordinary quantum mechanics which always assumes a fixed number of particles cannot describe such processes. The associated path integral has the same problem since it is a sum over a given set of particle orbits. Thus, even if relativistic kinematics is properly incorporated, a path integral cannot yield an accurate description of relativistic particles. An extension becomes necessary which includes an arbitrary number of mutually linked and branching fluctuating orbits…