Speaker
Description
Regularised field theories are usually described by assigning independent degrees of freedom to all modes below a UV cutoff. This gives a volume-scaling kinematical phase space. But for a given solution of the equations of motion, this count need not coincide with the number of independent canonical directions actually used by the dynamics.
I will present recent results on this question for a UV/IR-regulated classical scalar field. Using symplectic model order reduction, one can ask for the smallest Hamiltonian system that reproduces a field trajectory while preserving the symplectic structure. For the free theory, the answer is fixed by the number of distinct normal-mode frequencies. This gives area-type scaling in flat space and controlled curvature-dependent deviations on maximally symmetric backgrounds. Weak interactions smooth the sharp free-theory threshold, but numerical results suggest that the same scale persists over quasi-integrable time intervals.
The reduced phase space also changes the algebra of reconstructed field variables: many apparent modes are represented by fewer independent canonical variables, leading to induced overlap in their Poisson brackets. This provides a simple classical setting for separating apparent field-theoretic variables from dynamically independent degrees of freedom.