Causal Perturbative Quantum Field Theory and the Standard Model

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.

💡 Research Summary

The paper presents a rigorous construction of perturbative quantum field theory (pQFT) for the full Standard Model using the causal Epstein‑Glaser (EG) approach. Starting from the non‑relativistic evolution operator, the author recalls the Bogoliubov axioms—initial condition, symmetry, causality, unitarity, and translation invariance—and shows how these translate into the relativistic setting by replacing time variables with space‑time points and introducing test functions. The EG method is then employed as a recursive distribution‑splitting algorithm that builds the chronological products (T(A_1(x_1),\dots,A_n(x_n))) while preserving causality at each order.

A central technical innovation is the decomposition of chronological products into Wick sub‑monomials. Equations (1.21)–(1.22) express any product as a sum of normally ordered terms and vacuum‑average contributions (T_{00}). This separation makes the distinction between tree‑level (normal‑ordered) and loop‑level (vacuum‑average) contributions transparent already at second order: \