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

TL;DR

This paper explores the origin of zero point energy in quantum field theory, linking it to particle-antiparticle pairs, and derives pair production rates in external electric fields for various spins.

Contribution

It clarifies the physical origin of zero point energy and provides a derivation of pair production rates for charged bosons with arbitrary spin.

Findings

Zero point energy reflects particle-antiparticle content.

Derived pair production rate for charged bosons in electric fields.

Generalized results for particles of arbitrary spin.

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 $s$.