Representation of quantum field theory as classical statistical mechanics for field functionals (Q2477517)

Motivated by a century-long history of the question whether quantum mechanics is \textit{incomplete } since indeterministic, the article formulates a hidden variable theory for the second quantized Bose field by embedding it in a classical statistical model. Physical states are then represented by Gaussian measures on a very large phase space \(\Omega\), while physical variables are quadratic forms on \(\Omega\) respecting ist symplectic structure. That does not astonish the scientific world. Though mathematically correct, such an embedding is indeterministic. It does not solve the question whether there exists an underlying deterministic physical theory. Also, it seems unlikely that the formalism can be extended to include Fermions, i.e.\ the second quantized Dirac field.