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Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
General Relativity and Quantum Cosmology · Submitted 10 Apr 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Bulk charges are replaced by fluxes of superpotentials.
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The abstract, sentence by sentence
E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished one-dimensional subgroups are present. As a first illustration we propose a new {\it Affine action} that reduces to General Relativity upon gauge fixing the dilatation (Weyl 1918 like) part of the connection and elimination of auxiliary fields. It allows a comparison of most gravity superpotentials and we discuss their selection by the choice of boundary conditions. A second and independent application is a geometrical reinterpretation of the convection of vorticity in barotropic nonviscous fluids. We identify the one-dimensional subgroups responsible for the bulk charges and thus propose an impulsive forcing for creating or destroying selectively helicity. This is an example of a new and general Forcing Rule.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | E. | background 0.60 | 0.04 | 0.01 | unclear 1.00 |
| s1 | Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. | gap 0.73 | 0.20 | 0.19 | asserted 1.00 |
| s2 | Bulk charges are replaced by fluxes of superpotentials. | result 0.79 | 0.52 | 0.34 | asserted 1.00 |
| s3 | Gauge invariant bulk charges may subsist when distinguished one-dimensional subgroups are present. | result 0.93 | 0.56 | 0.19 | hedged possibility 1.00 |
| s4 | As a first illustration we propose a new {\it Affine action} that reduces to General Relativity upon gauge fixing the dilatation (Weyl 1918 like) part of the connection and elimination of auxiliary fields. | contribution 0.97 | 0.89 | 0.11 | asserted 0.76 |
| s5 | It allows a comparison of most gravity superpotentials and we discuss their selection by the choice of boundary conditions. | contribution 0.83 | 0.84 | 0.08 | asserted 0.94 |
| s6 | A second and independent application is a geometrical reinterpretation of the convection of vorticity in barotropic nonviscous fluids. | contribution 0.93 | 0.86 | 0.07 | asserted 0.99 |
| s7 | We identify the one-dimensional subgroups responsible for the bulk charges and thus propose an impulsive forcing for creating or destroying selectively helicity. | contribution 0.47 | 0.91 | 0.17 | asserted 0.96 |
| s8 | This is an example of a new and general Forcing Rule. | interpretation 0.45 | 0.71 | 0.14 | asserted 1.00 |
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The paper
Original abstract
E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished one-dimensional subgroups are present. As a first illustration we propose a new {\it Affine action} that reduces to General Relativity upon gauge fixing the dilatation (Weyl 1918 like) part of the connection and elimination of auxiliary fields. It allows a comparison of most gravity superpotentials and we discuss their selection by the choice of boundary conditions. A second and independent application is a geometrical reinterpretation of the convection of vorticity in barotropic nonviscous fluids. We identify the one-dimensional subgroups responsible for the bulk charges and thus propose an impulsive forcing for creating or destroying selectively helicity. This is an example of a new and general Forcing Rule.
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References
How the literature uses it
43 arXiv papers cite this in 71 sentences
Papers citing it · 48 sentences without a confident label
Builds on it 2 papers
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We think we can add to this result some new contributions, which will define the contents of our present paper: a) we provide with a new constructive derivation of the gauge symmetry, now obtained by using the Rosenfeld-Dirac-Bergmann (RDB) approach to gauge theories (constrained systems); b) we show that in the case of pure gravity the presence of this gauge symmetry imposes that the only connection that can be present in an observable must be the Levi Civita connection; c) we extend the results of [ref] to the case with fermions and show that, from the Einstein-Palatini point of view, the Einstein-Cartan theory is the natural extension of GR with fermionic matter; and d) we prove that the usual procedure beginning with a torsion free connection in the EP formalism, or a connection with metricity in the VEP formalism, is a consistent truncation of the original setting and it amounts to
On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection · Introduction · 0.94
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The discussion below is more or less trivial generalization of the argument about the boundary conditions proposed in [ref] .
Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA) · Conserved charges · 0.82
Uses its method or tool 6 papers
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We will see that the use of the symplectic structure and asymptotic charges advocated by Barnich, Brandt and one of the authors [ref] is crucial in obtaining the agreement[The relationship between cohomological methods [ref] and the closely related covariant methods based on the linear equations of motion [ref] and covariant symplectic methods in first order theories [ref] are detailed in Compere:2007az.].
Higher-Derivative Corrections to the Asymptotic Virasoro Symmetry of 4d Extremal Black Holes · Introduction · 0.99
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In order to study these quantities, we follow the route presented in [ref] .
Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form · General form of the superpotential · 0.99
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To derive Noether's currents we will go the standard way described, for example, in the works [ref] (see also Appendix in [ref] ).
Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA) · Local identities · 0.90
Compares with it 2 papers
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However, the unified way in which they are derived allows us to highlight the differences and the equivalences between different approaches as the covariant phase space methods of [ref] , the covariant methods inspired from the Hamiltonian prescription [ref] , Hamiltonian methods [ref] and methods based on the linearized Einstein equations [ref] .
Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions · Exact solutions and symmetries · 0.90
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The main differences between our definition ([ref]) and that given in [ref] are the following: (i) In [ref] the Lagrangian considered was the $ΓΓ-ΓΓ$ part of the Einstein-Hilbert action [ref] which is not covariant and hence the Noether current is not an tensor.
Noether Current, Horizon Virasoro Algebra and Entropy · Virasoro algebra and the central term · 0.98
Cites it as background 11 papers
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The Katz-Bicak-Lynden-Bell superpotential is the “covariantization" of Freud's superpotential and hence is based on a covariantization of Einstein's pseudo-tensor, see [ref] and [ref] or [ref] .
Einstein-Katz action, variational principle, Noether charges and the thermodynamics of AdS-black holes · Mass as a Noether charge · 0.84
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In first order formalism, the gauge symmetries of the gravitational theory consist of both diffeomorphism and local Lorentz transformation [ref] .
Null boundary gravitational charges from local Lorentz symmetries · Introduction · 0.86
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This problem has a long history and has been studied by many different authors in the context of General Relativity and other gauge theories of gravity (see, for example, discussions in [ref] and references therein).
Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA) · Introduction · 0.97
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