Counting DFF for literally interpreted gauge theories

Ascertain a correct procedure for counting dynamical functional freedom (DFF) in literally interpreted gauge theories, where dynamics are typically indeterministic, so that DFF can be consistently defined without defaulting to a gauge-invariant interpretation.

Background

The Henneaux–Teitelboim counting of degrees of freedom subtracts gauge degrees of freedom and so implicitly adopts a simply gauge-invariant interpretation, where physical states correspond to gauge orbits. Under a literal interpretation, where phase space points represent physical states and dynamics may be indeterministic, this subtraction may not be appropriate.

The authors discuss two possible approaches—count only empirically significant degrees of freedom (aligning with a gauge-invariant interpretation) or count all degrees of freedom from the full unconstrained phase space—but emphasize that, on a literal interpretation with indeterministic dynamics, it is not clear how to correctly define DFF. This ambiguity impacts the use of FF in equivalence arguments and the interpretation of gauge theories.