Can Euclidean lattice quantum field theory be analytically continued into Minkowski space?

TL;DR

This paper investigates whether Euclidean lattice quantum field theories can be analytically continued to Minkowski space, concluding that it is only possible in the continuum limit due to nonlocal effects introduced by discretization.

Contribution

It demonstrates that analytical continuation from Euclidean to Minkowski space requires taking the continuum limit because of nonlocal form factors caused by spacetime discretization.

Findings

Analytical continuation is impossible without the continuum limit.

Discretization introduces nonlocal form factors.

Wick rotation is infeasible in the lattice theory.

Abstract

In this paper, we attempt to test whether Euclidean lattice quantum field theory can be analytically continued into Minkowski space via the inverse Wick rotation. Our discussion indicates that such an analytical continuation is impossible without first taking the lattice theory to the continuum limit. The obstacle is that discretization of spacetime converts local quantum field theory into a theory with a nonlocal form factor, for which the Wick rotation is infeasible.