Model λ(φ 2n )4, n ≥ 2 quantum field theory: A nonstandard approach based on nonstandard pointwise-defined quantum fields

Abstract

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x, t), no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)4 exists and that the corresponding C* - algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ 2n )4, n ≥ 2 quantum field theory models are Lorentz covariant.