Dynamics and causality constraints in field theory

TL;DR

This paper explores how causality constraints in classical field theories have both geometric and dynamical implications, suggesting that finite, consistent theories should support fields on lightcone generators rather than just on the lightcone.

Contribution

It introduces a new perspective on causality in field theories, proposing that dynamical information emerges in the zero-distance limit and that consistent theories require fields supported on lightcone generators.

Findings

Infinities are linked to fields supported solely on the lightcone.

Fields supported on lightcone generators can lead to finite, consistent theories.

Causality constraints have both geometric and dynamical roles in field theory.

Abstract

We discuss the physical meaning and the geometric interpretation of causality implementation in classical field theories. Causality is normally implemented through kinematical constraints on fields but we show that in a zero-distance limit they also carry a dynamical information, which calls for a revision of our standard concepts of interacting fields. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the lightcone; a finite and consistent field theory requires a lightcone generator as the field support.