Energy-momentum tensors and stress tensors in geometric field theories

Abstract

Lagrangian field theories of geometric objects are the most natural framework for investigating the notion of general covariance. We discuss here geometric theories of interacting fields, depending on Lagrangians of arbitrary order, and we give general definitions of energy flow, partial energy flows, energy-momentum tensors, and stress tensors. We also investigate the role which energy-momentum tensors and stress tensors play in formulating the natural conservation laws associated with the second theorem of Noether. Examples of application may be found elsewhere. © 1985 American Institute of Physics.