Covariance of Time-Ordered Products Implies Local Commutativity of Fields

TL;DR

This paper demonstrates that Lorentz covariance of quantum field theories inherently implies microcausality, showing that local commutativity of fields follows from covariance of time-ordered products.

Contribution

It establishes that microcausality can be derived from Lorentz covariance through the covariance of time-ordered products, removing the need to assume it separately.

Findings

Lorentz covariance of Green's functions implies microcausality.

Microcausality is not an independent assumption but a consequence of covariance.

The formulation unifies covariance and causality in quantum field theory.

Abstract

We formulate Lorentz covariance of a quantum field theory in terms of covariance of time-ordered products (or other Green's functions). This formulation of Lorentz covariance implies spacelike local commutativity or anticommutativity of fields, sometimes called microscopic causality or microcausality. With this formulation microcausality does not have to be taken as a separate assumption.