Gauss' Law and Non-Linear Plane Waves for Yang-Mills Theory

Abstract

We investigate Non-Linear Plane-Wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the $SU(3)$ theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary non-zero mass and are exact extrema of the non-linear YM action. Among them, a unique harmonic plane wave with a non-trivial pattern in phase, spin and color is identified. Similar solutions are present in the $SU(4)$ case while are absent from the $SU(2)$ theory.

arXiv comment8 pages, 5 figures

References in corpus (2)

• Infrared Gluon and Ghost Propagators
• Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case

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