Symmetry properties under arbitrary field redefinitions of the metric energy–momentum tensor in classical field theories and gravity

Magnano, Guido; Sokołowski, Leszek M.

doi:10.1088/0264-9381/19/2/304

Cited by 14 publications

(49 citation statements)

References 21 publications

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“…The trivial gauge invariant Lagrangian L = 0, is the only gauge invariant expression. This is the expected result because spin-2 is well known to have an action which is gauge invariant only up to a surface term [9,6]. We can find this surface term by using integration by parts, leaving us with a total divergence and some remaining terms,…”

Section: A Procedures For Gauge Invariant Lagrangian Formulationsupporting

confidence: 52%

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics

Baker

Kuzmin

2019

Int. J. Mod. Phys. D

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A connection between linearized Gauss-Bonnet gravity and classical electrodynamics is found by developing a procedure which can be used to derive completely gauge invariant models. The procedure involves building the most general Lagrangian for a particular order of derivatives (N ) and rank of tensor potential (M ), then solving such that the model is completely gauge invariant (the Lagrangian density, equation of motion and energy-momentum tensor are all gauge invariant). In the case of N = 1 order of derivatives and M = 1 rank of tensor potential, electrodynamics is uniquely derived from the procedure. In the case of N = 2 order of derivatives and M = 2 rank of symmetric tensor potential, linearized Gauss-Bonnet gravity is uniquely derived from the procedure. The natural outcome of the models for classical electrodynamics and linearized Gauss-Bonnet gravity from a common set of rules provides an interesting connection between two well explored physical models.

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Section: A Procedures For Gauge Invariant Lagrangian Formulationsupporting

confidence: 52%

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics

Baker

Kuzmin

2019

Int. J. Mod. Phys. D

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“…(65) (10) is not gauge invariant. In fact, one can prove a general theorem [12] that the energy momentum tensor for the spin-2 field cannot be made gauge invariant for any choice of ψ cpq . This raises serious questions about whether the resulting theory after infinite iteration will possess any trace of the original gauge symmetry.…”

Section: Action and Energy Momentum Tensor For The Spin-2 Fieldmentioning

confidence: 99%

From Gravitons to Gravity: Myths and Reality

Padmanabhan

2008

Int. J. Mod. Phys. D

106

172

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There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full non-linear Einstein's theory of gravity by coupling a massless, spin-2 field h ab self-consistently to the total energy momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein-Hilbert action and (iii) it only uses standard concepts in Lorentz invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect -and critically re-examining several previous attempts -we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is impossible to obtain the Einstein-Hilbert (EH) action, starting from the standard action for gravitons in linear theory and iterating repeatedly. This result follows from the fact that EH action has a part (viz. the surface term arising from second derivatives of the metric tensor) which is non-analytic in the coupling constant, when expanded in terms of the graviton field. Thus, at best, one can only hope to obtain the remaining, quadratic, part of the EH Lagrangian (viz. the Γ 2 lagrangian) if no additional assumptions are made. Second, we use the Taylor series expansion of the action for Einstein's theory, to identify the tensor S ab , to which the graviton field h ab couples to the lowest order (through a term of the form S ab h ab in the lagrangian). We show that the second rank tensor S ab is not the conventional energy momentum tensor T ab of the graviton and provide an explanation for this feature. Third, we construct the full nonlinear Einstein's theory with the source being spin-0 field, spin-1 field or relativistic particles by explicitly coupling the spin-2 field to this second rank tensor S ab order by order and summing up the infinite series. Finally, we construct the theory obtained by self consistently coupling h ab to the conventional energy momentum tensor T ab order by order and show that this does not lead to Einstein's theory. The implications are discussed.

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“…A possible source of a further constraint is divergence of eq. (40). It may be shown by a direct calculation that if the equations (39) and (40) hold throughout the spacetime and if the five constraints are satisfied everywhere, then divergence of eq.…”

Section: The Four-dimensional Casementioning

confidence: 99%

“…(55) do not generate further constraints since their divergence vanishes identically providedR µν = 0 and π µν ;ν = 0. Secondly, one takes the limit m → 0 in the equations of motion (39) and (40). Since the scalar χ has already been eliminated, the resulting field equations,R µν = 0 and (55), represent the full set of solutions rather than a special class; the five constraints hold.…”

Section: Massless Spin-two Field In Hjfmentioning

confidence: 99%

“…where Ψ ≡ η µν Ψ µν [37,17,30,39,40]. In contrast, the linearized theory for the field Φ µν above is not self-contained as a theory for a free spin-two field in a fixed background (in particular, it has not its own Lagrangian) and arises only as a limit case of the nonlinear theory based on the Helmholtz Lagrangian (66) and (76).…”

Section: Internal Structure Of the Theory In Efmentioning

confidence: 99%

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Nonlinear massive spin-2 field generated by higher derivative gravity

Magnano

Sokołowski

2003

Annals of Physics

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We present a systematic exposition of the Lagrangian field theory for the massive spin-two field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well known inconsistency of the theory for a linear massive spin-two field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called "(Helmholtz-)Jordan frame" and "Einstein frame". In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-two field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-two field in Einstein frame are given, and a simple but nontrivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-two field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-two field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.

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Symmetry properties under arbitrary field redefinitions of the metric energy–momentum tensor in classical field theories and gravity

Cited by 14 publications

References 21 publications

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics

From Gravitons to Gravity: Myths and Reality

Nonlinear massive spin-2 field generated by higher derivative gravity

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