Mass gap v.s. classical nonlinear Yang-Mills waves

Question

Why people said (Witten, p. 11),

"For Yang-Mills theory. the mass gap is the reason that we do not see classical nonlinear Yang-Mills waves. They are a good approximation only under inaccessible conditions"

1. Above the energy / mass gap, should we still see the classical nonlinear Yang-Mills waves?

2. In the spin system, for example, couldn't we still see the spin wave above the massive spin gap? Could it have linear dispersion or high order non-linear dispersion?

This post imported from StackExchange Physics at 2020-10-29 11:41 (UTC), posted by SE-user annie marie heart

Comments

The mass gap exists in confined systems, and obviously in a confined system there are no classical waves since the particles cannot travel far enough to create them. Whether waves can exist in a quark-gluon plasma, where the system is deconfined, is an interesting question ...

This post imported from StackExchange Physics at 2020-10-29 11:41 (UTC), posted by SE-user John Rennie

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Non-linear waves are perfectly legal solutions of the classical Yang-Mills equations (see here where the ongoing discussion between me and Terry Tao was finally settled). These could be used in principle as the ground state for a quantum theory. In such a case, instantons could play a relevant role. Such classical waves have a massive dispersion relation.

This post imported from StackExchange Physics at 2020-10-29 11:41 (UTC), posted by SE-user Jon