On the Interaction in Lattice Gauge Theory

TL;DR

This paper discusses how discretizing spacetime in lattice gauge theory can restore the interaction picture, which is absent in continuous Lorentz-invariant quantum field theories due to Haag's theorem.

Contribution

It highlights that lattice discretization makes the quantum field theory reducible, thereby enabling the reintroduction of the interaction picture.

Findings

Discretization of spacetime affects the reducibility of the quantum field theory.

Lattice gauge theory can circumvent Haag's theorem.

Interaction picture is restored on the lattice.

Abstract

Haag's theorem states that if a quantum field theory is Lorentz invariant and irreducible, there is no interaction picture. But if we construct quantum field theory on a discrete lattice spacetime, its representation will be reducible and the interaction picture will be restored again.