Covariant noether identities in covariant field theories

Ray, John R.

doi:10.1007/bf02820284

Cited by 6 publications

(5 citation statements)

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“…To present covariant expressions one includes either additional structures, or uses relevant reformulations. One of the earlier attempts to suggest covariantized Noether identities in GR is the Ray work [25]. Here, in a definite sense, we develop Ray's ideas.…”

Section: Introductionmentioning

confidence: 88%

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Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

Петров

Lompay

2012

Gen Relativ Gravit

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A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized Noether identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical Noether and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein-Gauss-Bonnet gravity. Using all the superpotentials of the family gives the standard accepted mass.

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Section: Introductionmentioning

confidence: 88%

“…Below, with using the new form of the Lagrangian (29) and the connections between partial and covariant derivatives (25) and (26) we show that the new coefficients (38) - (40) are represented in an explicitly covariant form. Let us begin from the last the coefficient (40).…”

Section: A Direct Application Of the Noether Proceduresmentioning

confidence: 94%

Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

Петров

Lompay

2012

Gen Relativ Gravit

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“…When the gauge field is treated as an external or background field, it is actually possible to reconcile the gauge symmetry with the Noether's theorem [57,58,59,60,61,62]. The origin of the problem comes from the fact that the standard approach deals with quantities that are not gauge covariant, and therefore ill-defined from the geometrical point of view.…”

Section: Gauge-covariant Approachmentioning

confidence: 99%

Gauge-covariant canonical formalism revisited with application to the proton spin decomposition

Lorcé¹

2013

Phys. Rev. D

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We revisit the gauge-covariant canonical formalism by separating explicitly physical and gauge degrees of freedom. We show in particular that the gauge-invariant linear and angular momentum operators proposed by Chen et al. can consistently be derived from the standard procedure based on Noether's theorem. Finally, we demonstrate that this approach is essentially equivalent to the gauge-invariant canonical formalism based on the concept of Dirac variables. Because of many similarities with the background field method, the formalism developed here should also be relevant to general relativity and any metric theories.

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“…Substituting (35) and (36) into formula (34), then into (24), one obtains an equivalent representation of the general Noether identity:…”

Section: The Klein and Noether Identitiesmentioning

confidence: 99%

“…Frequently, such a covariantization is based on including an auxiliary structure, like a background metric, see, for example, Refs. [36][37][38] and also recent works (Refs. 39,40 ).…”

Section: Introductionmentioning

confidence: 99%

Covariant differential identities and conservation laws in metric-torsion theories of gravitation. I. General consideration

Lompay

Петров

2013

Journal of Mathematical Physics

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Arbitrary diffeomorphically invariant metric-torsion theories of gravity are considered. It is assumed that Lagrangians of such theories contain derivatives of field variables (tensor densities of arbitrary ranks and weights) up to a second order only. The generalized Klein-Noether methods for constructing manifestly covariant identities and conserved quantities are developed. Manifestly covariant expressions are constructed without including auxiliary structures like a background metric. In the Riemann-Cartan space, the following manifestly generally covariant results are presented: (a) The complete generalized system of differential identities (the Klein-Noether identities) is obtained. (b) The generalized currents of three types depending on an arbitrary vector field displacements are constructed: they are the canonical Noether current, symmetrized Belinfante current and identically conserved Hilbert-Bergmann current. In particular, it is stated that the symmetrized Belinfante current does not depend on divergences in the Lagrangian. (c) The generalized boundary Klein theorem (third Noether theorem) is proved. (d) The construction of the generalized superpotential is presented in details, and questions related to its ambiguities are analyzed.

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Covariant noether identities in covariant field theories

Cited by 6 publications

References 1 publication

Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

Gauge-covariant canonical formalism revisited with application to the proton spin decomposition

Covariant differential identities and conservation laws in metric-torsion theories of gravitation. I. General consideration

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