Gauss’ law and nonlinear 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.

A non-abelian quasi-particle model for gluon plasma

“…Nevertheless, this space contains the basic ingredient of the non-abelian character, namely the non-linearity due to the gauge field self-interaction. A recent publication [35] has found a larger class of S U(3) plane wave solutions which could in principle be included in the present model. However, these solutions possess an infinite countable set of periods in contrast to the solutions in the S U (2) subspace which have fixed period P = 5.244.…”

Quantum stability of nonlinear wave type solutions with intrinsic mass parameter in QCD

“…wheren = r/r [46][47][48][49][50]. Note, the "hedgehog" ansatz (29) is related to the ansatz (27) by an appropriate singular gauge transformation [51]. We prefer to use the ansatz (27) in the so-called Abelian gauge [51] since such a representation allows to inteprete the our monopole solution as a static Wu-Yang monopole interacting to dynamic off-diagonal gluons presented by the filed ψ(r, t).…”

“…In particular, we are interested in such a classical solution which are stable against quantum gluon fluctuations. A known class of non-linear plane wave solutions with a mass scale and zero spin [25][26][27][28][29][30] is of primary interest in our search of possible stable vacuum fields since one expects that a system of massive spinless particles can form a stable condensate in the classical theory. The presence of spinless states can help in removing the Nielsen-Olesen instability.…”

“…The presence of spinless states can help in removing the Nielsen-Olesen instability. We consider a special plane wave solution in SU (2) Yang-Mills theory which possesses a spherically symmetric configuration in the rest frame [25][26][27][28][29][30]. A simple ansatz for non-vanishing components of the gauge potential reads…”

“…Such a stable field configuration can serve as a structure element in further construction of a true QCD vacuum. There is a wide class of known stationary non-linear wave solutions [25][26][27][28][29][30] which possess non-trivial features: the presence of mass scale parameters, non-vanishing longitudinal components of color fields along the propagation direction, color magnetic charge and vanishing classical spin density operator. This gives a hint that some of such classical solutions describe quantum states corresponding to massive spinless quasi-particles which might lead to formation of a stable vacuum condensate.…”