Quantum gravity with purely virtual particles from asymptotically local quantum field theory

TL;DR

This paper introduces asymptotically local quantum field theories (AL-QFTs) that smoothly connect nonlocal models to local limits in Minkowski spacetime, featuring purely virtual particles and potential applications in quantum gravity.

Contribution

It identifies a class of AL-QFT models with regular local limits in Minkowski space, incorporating purely virtual particles and extending to quantum gravity.

Findings

AL-QFT models have well-behaved local limits in Minkowski spacetime.

Nonlocal deformations generate purely virtual particles in Feynman diagrams.

The framework can be applied to quantum gravity and offers new approaches to off-shell physics.

Abstract

We investigate the relationship between nonlocal and local quantum field theories, and search for a viable notion of "local limit" to relate the unitary models. In Euclidean space it is relatively easy to have nonlocal theories with well-behaved local limits. In Minkowski spacetime, instead, singular behaviors are generically expected. Relaxing some assumptions on the "form factors" considered in the literature, we identify a class of models that have regular local limits in Minkowski spacetime. We call the models "asymptotically local" quantum field theories (AL-QFTs) and show that their limits are theories with physical and purely virtual particles (PVPs). In the bubble diagram, the nonlocal deformation generates PVPs straightforwardly. In the triangle diagram, it does so possibly up to multi-threshold corrections, which may be adjusted by tuning the deformation itself. We also build an asymptotically local deformation of quantum gravity with purely virtual particles. AL-QFT can serve various purposes, such as suggesting innovative approaches to off-shell physics, providing an alternative formulation for theories with PVPs, or smoothing out nonanalytic behaviors. We discuss its inherent arbitrariness and the implications for renormalizability.