Field theory and weak Euler-Lagrange equation for classical particle-field systems

Hong Qin, Joshua W. Burby, and Ronald C. Davidson
Phys. Rev. E 90, 043102 – Published 6 October 2014

Abstract

It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.

  • Received 3 May 2014
  • Revised 11 September 2014

DOI:https://doi.org/10.1103/PhysRevE.90.043102

©2014 American Physical Society

Authors & Affiliations

Hong Qin1,2, Joshua W. Burby2, and Ronald C. Davidson2

  • 1Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 2Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 4 — October 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×