Counting functional freedom for quantum theories

Develop a rigorous method to count functional freedom (FF) for quantum theories, beyond the constrained-Hamiltonian counting available for classical field theories, so that FF can be meaningfully applied in quantum contexts such as string theory.

Background

The paper reconstructs Penrose’s notion of functional freedom (FF) and gives it a rigorous footing for classical field theories via the constrained Hamiltonian framework, where degrees of freedom are counted using first- and second-class constraints. However, this approach only covers theories that admit a Hamiltonian formulation and, crucially, only classical theories.

The authors note that extending FF to quantum theories is problematic. A tempting move is to identify the FF of a quantum theory with that of a corresponding classical theory obtained by quantization, but this fails in general: not all quantum theories arise from quantizing a classical theory, and strong–weak coupling dualities can yield multiple, inequivalent classical limits. Hence, a principled quantum FF counting method is needed, particularly for applications to string theory where FF features in arguments about equivalence and consistency.