Counting dynamical functional freedom under literal interpretations of gauge theories

Develop a coherent and precise method for counting dynamical functional freedom (DFF) in gauge theories under a literal interpretation in which physical states correspond to points in the unconstrained phase space and dynamics is indeterministic, clarifying how such indeterminism affects the FF/DFF count.

Background

The authors discuss interpretative stances for gauge theories (literal, simply gauge-invariant, coarse-grained gauge-invariant) and note that standard constrained-Hamiltonian counting subtracts gauge degrees of freedom, effectively aligning with a gauge-invariant interpretation.

Under a literal interpretation, physical states correspond to points in the full phase space and dynamics can be indeterministic; the authors argue that their constrained-Hamiltonian counting does not capture these physical degrees of freedom and that it is unclear how to correctly count DFF in such cases.

They outline two possible approaches—count all degrees of freedom from the full unconstrained phase space or count only empirically significant degrees—but emphasize that a satisfactory, principled resolution is lacking.