Stability and causality of multi-local theories

Strasbourg University, High Energy Theory Group, CNRS-IPHC - 23 rue du Loess, BP28, 67037 Strasbourg Cedex 2 France

Received: 11 October 2017
Accepted: 20 January 2018

Abstract

The regularized theories are non-local at the scale of the cutoff, leading so to the usual difficulties of non-local theories. In this work the conservation laws and causality are investigated for classical field theories with multi-cluster action. The conservation laws are found to play a less significant role than in local theories because due to the non-locality the conserved quantities are not integrals of the motion, and they can exist even without underlying symmetries. Moreover, the conservation of the energy cannot prevent the instability brought about by the unbounded nature of the energy from below. Hence a sufficient condition of stability is lost. Theories, obtained by appropriate point splitting of local interactions are shown to be causal thereby a necessary condition of stability can be retained.