Relativistic invariance of the vacuum

TL;DR

This paper provides a direct, general proof of the relativistic invariance of vacuum correlations in quantum field theories, based on the closed time path formalism and fundamental principles, without relying on the Wightman axioms.

Contribution

It offers a novel, axioms-independent proof of vacuum invariance in relativistic quantum field theories using the closed time path formalism.

Findings

Vacuum correlations are invariant under Lorentz transformations.

The proof is perturbative and allows for potential spontaneous symmetry breaking.

Time symmetry is explicitly violated in the framework.

Abstract

Relativistic invariance of the vacuum is (or follows from) one of the Wightman axioms which is commonly believed to be true. Without these axioms, here we present a direct and general proof of continuous relativistic invariance of all real-time vacuum correlations of fields, not only scattering (forward in time), based on closed time path formalism. The only assumptions are basic principles of relativistic quantum field theories: the relativistic invariance of the Lagrangian, of the form including known interactions (electromagnetic, weak and strong), and standard rules of quantization. The proof is in principle perturbative leaving a possibility of spontaneous violation of invariance. Time symmetry is however manifestly violated.