Equivalence of Classical Statistics and Quantum Dynamics of Well-Posed Bosonic Field Theories

Abstract

Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement operator. A previous paper defined a classical density matrix R encoding the statistical moments of an ensemble of states of classical second-order Hamiltonian field theory. It proved Tr(RQ)=E(Q), etc., for the usual field operators as defined by Weinberg, and it proved that those observables of the classical system obey the usual Heisenberg dynamic equation. However, R itself obeys dynamics different from the usual Liouville equation! This paper derives those dynamics and the discrepancy between CFT and normal form QFT in predicting any observables g(Q,P). There is some preliminary evidence for the conjecture that the discrepancies disappear in equilibrium states (bound states and scattering states) for finite bosonic field theories. Even if not, they appear small enough to warrant reconsideration of CFT as a theory of dynamics. Appendix proposes alternative closure of turbulence based on modified Bogliubov transforms, an application where ordinary ones become undefined.