On the Origins of the Planck Zero Point Energy in Relativistic Quantum Field Theory

Abstract

It is argued that the zero point energy in quantum field theory is a reflection of the particle anti-particle content of the theory. This essential physical content is somewhat disguised in electromagnetic theory wherein the photon is its own anti-particle. To illustrate this point, we consider the case of a charged Boson theory $(\pi^+,\pi^-)$ wherein the particle and anti-particle can be distinguished by the charge $\pm e$. Starting from the zero point energy, we derive the Boson pair production rate per unit time per unit volume from the vacuum in a uniform external electric field. The result is further generalized for arbitrary spin $s$.