# How is BRST symmetry related to local integrals of motion?

I'm hoping someone can confirm or check my reasoning below:

In this wiki, they describe caos in a classical system as the spontaneous symmetry breaking of a BRST.

In this stackexchange, they clarify that the BRST symmetry is simply the gauge theory.

I understand chaos as the result of a lack of local integrals of motion. So my understanding of the statement in the wiki is this:

They are defining a stochastic path integral for a many body system to get a corresponding quantum field theory. This path integral then has local integrals of motion which correspond to the local gauge or BRST symmetry. Therefore the spontaneous breaking of these local integrals of motion in the development of caos corresponds to breaking of the gauge symmetry.

Breaking gauge symmetry makes me uncomfortable, but I'm somewhat ok with that because the classical theory doesn't haven't a gauge invariance.

Anyways, is this reasoning correct? Am I missing something?