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

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

2009-03-13

arxiv.org/abs/0903.2357v4

Mod. Phys. Lett. A 24, 2425-2432 (2009)

Physics

Mathematical Physics

6 pages. Added thanks to Terence Tao. This paper responds to a criticism by him to the mapping theorem presented in arXiv:0709

Scientific paper

10.1142/S021773230903165X

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. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.

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