Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories

Abstract

We discuss the relation between canonical and metric energy-momentum tensors for field theories with actions that can depend on the higher derivatives of tensor fields in a flat spacetime. In order to obtain it we use a modification of the Noether's procedure for curved space-time. For considered case the difference between these two tensors turns out to have more general form than for theories with no more than first order derivatives. Despite this fact we prove that the difference between corresponding integrals of motion still has the form of integral over 2-dimensional surface that is infinitely remote in the spacelike directions.

arXiv commentLaTeX, 11 pages

References in corpus (6)

• Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity
• Gravity as a field theory in flat space-time
• Constraint algebra for Regge-Teitelboim formulation of gravity
• General Relativity à la string: a progress report
• The Energy-Momentum Tensor in General Relativity and in Alternative Theories of Gravitation, and the Gravitational vs. Inertial Mass
• Gravitational energy in the framework of embedding and splitting theories

Cited by in corpus (4)

• Phonon and Shifton from a Real Modulated Scalar
• A gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
• Equality of the Hilbert Hamiltonian and the canonical Hamiltonian for gauge theories in a static spacetime