Chaotic quantization of field theories

Abstract

We introduce a class of coupled map lattices that simulate quantum field theories in an appropriate scaling limit. The Parisi-Wu approach of stochastic quantization is extended to more general spatio-temporal stochastic processes generated by coupled chaotic dynamical systems. We show that such complicated processes can intrinsically arise from a quantized Phi 4-theory with formally infinite bare coupling parameters. This field theory leads to a lattice of diffusively coupled cubic maps, for example, coupled third-order Tschebyscheff polynomials. We calculate effective potentials for this model. The effective potentials turn out to exhibit interesting transition scenarios when the spatial coupling strength is changed: there are several 'critical points' where single-wells change into double-wells. We point out a possible application of our approach in cosmology: The equation of motion of the inflaton field, when quantized by the Parisi-Wu method, reduces to just the type of coupled map lattices studied here, provided the bare mass and bare quartic coupling approach infinity.