Nonlocal Lagrangians for Accelerated Systems

TL;DR

This paper develops a Lorentz-invariant nonlocal Lagrangian framework for accelerated systems in Minkowski spacetime, deriving equations of motion via a variational principle and exploring implications for electromagnetic and Dirac fields.

Contribution

It introduces a novel nonlocal Lagrangian formulation for accelerated systems, extending local field theories to account for acceleration-induced nonlocality.

Findings

Derived nonlocal equations of motion from a variational principle.

Constructed nonlocal Lagrangian by composing local inertial Lagrangian with nonlocal transformation.

Discussed implications for electromagnetic and Dirac fields.

Abstract

Acceleration-induced nonlocality and the corresponding Lorentz-invariant nonlocal field equations of accelerated systems in Minkowski spacetime are discussed. Under physically reasonable conditions, the nonlocal equation of motion of the field can be derived from a variational principle of stationary action involving a nonlocal Lagrangian that is simply obtained by composing the local inertial Lagrangian with the nonlocal transformation of the field to the accelerated system. The implications of this approach for the electromagnetic and Dirac fields are briefly discussed.