Noether currents and charges for Maxwell-like Lagrangians

Abstract

Hilbert-Noether theorem states that a current associated to diffeomorphism invariance of a Lagrangian vanishes on shell modulo a divergence of an arbitrary superpotential. Application of the Noether procedure to physical Lagrangians yields, however, meaningful (and measurable) currents. The well known solution to this ``paradox'' is to involve the variation of the metric tensor. Such procedure, for the field considered on a fixed (flat) background, is sophisticated logically (one need to introduce the variation of a fixed field) and formal. We analyze the Noether procedure for a generic diffeomorphism invariant $p$-form field model. We show that the Noether current of the field considered on a variable background coincides with the current treated in a fixed geometry. Consistent description of the canonical energy-momentum current is possible only if the dynamics of the geometry (gravitation) is taken into account. However, even the ``truncated'' consideration yields the proper expression. We examine the examples of the free $p$-form gauge field theory, the GR in the coframe representation and the metric-free electrodynamics. Although, the variation of a metric tensor is not acceptable in the latter case, the Noether procedure yields the proper result.

20 pages, version to appear in Journal of Physics A

References in corpus (18)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
• Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
• Energy-Momentum Conservation in General Relativity
• Quasilocal quantities for GR and other gravity theories
• Asymptotic conservation laws in field theory
• Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity
• Characteristic cohomology of $p$-form gauge theories
• Energy-momentum current for coframe gravity
• A small guide to variations in teleparallel gauge theories of gravity and the Kaniel-Itin model
• Noether Charges, Brown-York Quasilocal Energy and Related Topics
• Generally covariant Fresnel equation and the emergence of the light cone structure in linear pre-metric electrodynamics
• Another positivity proof and gravitational energy localizations

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