How to quantize a gauge theory which is invariant on-shell?

The Yang-Mills gauge theory is invariant under gauge transformations.
But there are certain non-Yang-Mills gauge theories which are invariant
ON-SHELL under gauge transformations. It means that the action is gauge
invariant only if the equation of motion is satisfied.

One would assume that the quantization procedure would be different for
such gauge theories. Would the BRST symmetry survive after quantizaton?
Or would BRST symmetry be on-shell too? Can anyone provide some
references on this topic?

Max

.

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