The Field Structure of Free Photons

TL;DR

This paper demonstrates that the vector potential of a photon has a discrete frequency and energy spectrum, extending the analysis to multi-photon systems and introducing a new tool for quantum field theory wave-functional analysis.

Contribution

It provides a theoretical proof that photon vector potentials have discrete frequency and energy spectra, and extends this to multi-photon systems, introducing a new analytical approach.

Findings

Photon vector potential has a delta function spectrum at a specific frequency.

Multi-photon systems have a sinusoidal vector potential with energy n times that of a single photon.

Introduces a simple tool using Parseval's theorem for analyzing quantum field theory wave-functionals.

Abstract

Using a quantum field theoretic description of the photon it is shown that, as intuitively expected but not before theoretically proven, the vector potential of a photon has a likely amplitude associated with a discrete frequency and therefore energy, and momentum. In particular, by finding the wave-functional for the vector potential, it is shown that the likely absolute amplitude spectrum has delta function at a given frequency. This analysis is extended to n-photon systems. It shows that such systems have a vector potential distribution whose most likely element has a strong sinusoidal component which has an amplitude corresponding to n-fold more energy than a single photon system. An analogous result for photons of different energy is also derived. Through the use of Parseval's theorem for stochastic systems, the calculations and associated analyses introduces a simple tool for exploring the nature of QFT Schrodinger wave-functional generally.