We introduce symplectic quantization, a novel functional approach to quantum field theory which
allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with
all the traditional importance sampling protocols, well defined only for Euclidean Field Theory.
This importance sampling procedure is realized by means of a deterministic dynamics generated
by Hamilton-like equations evolving with respect to an auxiliary time parameter $\tau$. In this
framework, expectation values over quantum fluctuations are computed as dynamical averages
along the trajectories parameterized by $\tau$. Assuming ergodicity, this is equivalent to sample
a microcanonical partition function. Then, by means of a large-M calculation, where M is
the number of degrees of freedom on the lattice, we show that the microcanonical correlation
functions are equivalent to those generated by a Minkowskian canonical theory where quantum
fields fluctuations are weighted by the factor $exp(S/\hbar)$, with š¯‘† being the original relativistic action
of the system [1].
