Abstract
A procedure to define the Becchi-Rouet-Stora-Tyutin (BRST) charge from the Noether one in extended phase space is given. It is outlined how this prescription can be applied to a Friedmann-Robertson-Walker space-time with a differential gauge condition and it allows us to reproduce the results of Ref. [21]. Then, we discuss the cohomological classes associated with functions in extended phase space having ghost number one and we recover the frozen formalism for classical observables. Finally, we consider the quantization of Becchi-Rouet-Stora-Tyutin--closed states and we define a scalar product which implements the super-Hamiltonian constraint.
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