Symplectic quantization: A new deterministic approach to the dynamics of quantum fields inspired by statistical mechanics*

In this contribution we summarize the main features of a new algorithm (already presented in [1]) to sample numerically on the lattice the quantum fluctuations of fields by means of a deterministic pseudo-Hamiltonian dynamics in an enlarge space of variables. The main goal is to provide a numerical tool which is well defined in Minkowski space. The proposed approach introduces an additional time variable that plays the role of a true physical parameter that controls the deterministic dynamics. The sampling of quantum fluctuations is guaranteed by the presence of new additional conjugated momenta, which represent the rate of variation of ordinary fields with respect to the newly added time variable. From the pseudo-Hamiltonian dynamics one is then able, assuming ergodicity, to retrieve the Feynman path integral as the Fourier transform of a pseudo-microcanonical partition function.