Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case

Understand

We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level.

• It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion.
• In this limit the theories share the spectrum, at the leading order, that is the one of an harmonic oscillator.
• Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space.