Augmented quantum field theory: A proposal to extend conventional formulations

Abstract

An alternative approach to scalar field quantization is proposed and analyzed, particularly for ${\left({\varphi }^4\right)}_n$ models, $n\ge 2$. Without altering the classical equation of motion at all, the action is "augmented" by an additional term that in effect induces a new measure in a functional integration approach to quantization. Guided by specialized soluble models, a lattice-space formulation is proposed for covariant theories for which in the continuum limit the truncated four-point correlation function is non-negative in contrast to the conventional formulation. Besides suggesting nontrivial behavior for $n\ge 4$, the augmented models lead to new noncanonical solutions for $n=2, 3$. All solutions of the augmented models are disconnected from those of the conventional approach in the sense that the augmented models pass to a pseudofree model differing from the free model as the nonlinear coupling constant vanishes.