Speaker
Description
We introduce Symplectic Quantization, a novel functional approach to quantum field theory that makes it possible to sample quantum fluctuations directly in Minkowski space--time, thus bypassing the limitations of traditional importance-sampling methods restricted to imaginary time. The technique is based on a deterministic dynamics governed by Hamilton-like equations in an auxiliary time parameter, which generates a microcanonical ensemble of field configurations. We prove that microcanonical correlation functions obtained in this formulation are equivalent to those of a Minkowskian canonical theory, where quantum fluctuations are weighted by the oscillatory factor $e^{iS}$, with $S$ the original action. We test the method on two representative systems. For the quantum harmonic oscillator, we reconstruct the full real-time dynamics not only of the ground state but also of excited states and quantum superpositions, accurately reproducing expectation values and interference phenomena that are inaccessible to Euclidean approaches. For a free scalar field theory in $1+1$ dimensions, we recover the complete structure of real-time quantum field theory, including the Feynman propagator, the Schwinger--Dyson equations and their contact terms, thereby clarifying the role of the generalized Hamilton equations within this framework.
These results show that Symplectic Quantization reproduces the full real-time quantum dynamics of both quantum-mechanical and field-theoretical systems with high accuracy, providing a solid foundation for future applications to interacting quantum field theories.