Ghost-free infinite derivative quantum field theory

TL;DR

This paper explores Lorentz-invariant infinite derivative quantum field theories that introduce non-local interactions at high energy scales, leading to acausal effects confined within the non-locality region, and potentially resolving ultraviolet singularities.

Contribution

It provides a detailed analysis of non-local modifications to quantum field theories without introducing new dynamical degrees of freedom, highlighting their implications for causality and ultraviolet behavior.

Findings

Green functions are modified with non-local terms causing acausality.

Non-locality violates local commutativity but is confined within the non-locality scale.

Non-local theories can ameliorate ultraviolet singularities in quantum field theory.

Abstract

In this paper we will study Lorentz-invariant, infinite derivative quantum field theories, where infinite derivatives give rise to non-local interactions at the energy scale $M_s$, beyond the Standard Model. We will study a specific class, where there are no it new dynamical degrees of freedom other than the original ones of the corresponding local theory. We will show that the Green functions are modified by a non-local extra term that is responsible for acausal effects, which are confined in the region of non-locality, i.e. $M_s^{-1}.$ The standard time-ordered structure of the causal Feynman propagator is not preserved and the non-local analog of the retarded Green function turns out to be non-vanishing for space-like separations. As a consequence the local commutativity is violated. Formulating such theories in the non-local region with Minkowski signature is not sensible, but they have Euclidean interpretation. We will show how such non-local construction ameliorates ultraviolet/short-distance singularities suffered typically in the local quantum field theory. We will show that non-locality and acausality are inherently off-shell in nature, and only quantum amplitudes are physically meaningful, so that all the perturbative quantum corrections have to be consistently taken into account.