A semi-classical Quantum Field Theory?
Revolution will not be televised
(but it will be on video).
A semi-classical quantization of Quantum Field Theory
would use the exact, non-perturbative unstable solutions of the classical equations
as WKB, saddle-point approximations to the quantum Van Vleck
/ Gutzwiller propagators:
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Within the last few years our understanding of numerically exact,
non-perturbative solutions of Navier-Stokes equations, the most
studied classical field theory, has made great strides.
The theory triangulates
the infinite-dimensional Navier-Stokes state space (not low-dimensional models)
by sets of exact solutions (equilibria, traveling waves, periodic orbits, ...) which
form a rigid backbone which enables us to describe the
sinuous motions of a turbulent field.
These solutions and their inter-relations are more profitably visualized in
the infinite-dimensional state space than as fields over 3-dimensional
configuration space.
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