Causal Perturbative Quantum Field Theory and the Standard Model

TL;DR

This paper develops a rigorous framework for perturbative quantum field theory in the Standard Model, establishing gauge invariance proofs for both tree-level and loop contributions across various field types.

Contribution

It provides a mathematically rigorous formulation of perturbative QFT for the Yang-Mills model, including proofs of gauge invariance at second order.

Findings

Rigorous description of chronological products using Wick submonomials

Proof of gauge invariance for tree and loop contributions

Framework applicable to massless and massive vector, scalar, and Dirac fields

Abstract

We consider the general framework of perturbative quantum field theory for the general Yang-Mills model including massless and massive vector fields and also scalar and Dirac fields. We describe the chronological products using Wick submonomials and give rigorous proofs of gauge invariance for tree and loop contributions in the second order of the perturbation theory.