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Universal Field Equations with Reparametrisation Invariance
High Energy Physics - Theory · Submitted 17 Feb 1992
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim New reparametrisation invariant field equations are constructed which describe $d$-brane models in a space of $d+1$ dimensions.
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The abstract, sentence by sentence
New reparametrisation invariant field equations are constructed which describe $d$-brane models in a space of $d+1$ dimensions. These equations, like the recently discovered scalar field equations in $d+1$ dimensions, are universal, in the sense that they can be derived from an infinity of inequivalent Lagrangians, but are nonetheless Lorentz (Euclidean) invariant. Moreover, they admit a hierarchical structure, in which they can be derived by a sequence of iterations from an arbitrary reparametrisation covariant Lagrangian, homogeneous of weight one. None of the equations of motion which appear in the hierarchy of iterations have derivatives of the fields higher than the second. The new sequence of Universal equations is related to the previous one by an inverse function transformation. The particular case of $d=2$, giving a new reparametrisation invariant string equation in 3 dimensions is solved.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | New reparametrisation invariant field equations are constructed which describe $d$-brane models in a space of $d+1$ dimensions. | contribution 0.99 | 0.94 | 0.58 | asserted 1.00 |
| s1 | These equations, like the recently discovered scalar field equations in $d+1$ dimensions, are universal, in the sense that they can be derived from an infinity of inequivalent Lagrangians, but are nonetheless Lorentz (Euclidean) invariant. | result 0.52 | 0.67 | 0.32 | asserted 1.00 |
| s2 | Moreover, they admit a hierarchical structure, in which they can be derived by a sequence of iterations from an arbitrary reparametrisation covariant Lagrangian, homogeneous of weight one. | result 0.60 | 0.85 | 0.15 | asserted 1.00 |
| s3 | None of the equations of motion which appear in the hierarchy of iterations have derivatives of the fields higher than the second. | result 0.98 | 0.84 | 0.09 | asserted 1.00 |
| s4 | The new sequence of Universal equations is related to the previous one by an inverse function transformation. | result 0.72 | 0.76 | 0.11 | asserted 1.00 |
| s5 | The particular case of $d=2$, giving a new reparametrisation invariant string equation in 3 dimensions is solved. | result 0.78 | 0.91 | 0.15 | asserted 1.00 |
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The paper
Original abstract
New reparametrisation invariant field equations are constructed which describe $d$-brane models in a space of $d+1$ dimensions. These equations, like the recently discovered scalar field equations in $d+1$ dimensions, are universal, in the sense that they can be derived from an infinity of inequivalent Lagrangians, but are nonetheless Lorentz (Euclidean) invariant. Moreover, they admit a hierarchical structure, in which they can be derived by a sequence of iterations from an arbitrary reparametrisation covariant Lagrangian, homogeneous of weight one. None of the equations of motion which appear in the hierarchy of iterations have derivatives of the fields higher than the second. The new sequence of Universal equations is related to the previous one by an inverse function transformation. The particular case of $d=2$, giving a new reparametrisation invariant string equation in 3 dimensions is solved.
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References
How the literature uses it
8 arXiv papers cite this in 8 sentences
Papers citing it · 5 sentences without a confident label
Cites it as background 3 papers
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Galileon Lagrangians are quite peculiar: they involve second derivatives, but the corresponding field equations are nevertheless of the second order [ref] .
Cosmological bounces and Lorentzian wormholes in Galileon theories with an extra scalar field · Introduction · 0.96
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The construction and complete classification of these models in arbitrary dimensions was achieved in [ref] , although they have actually been known, at least in four or less dimensions, since much before [ref] (see e.g. [ref] for a review of their formal aspects).
Classifying Galileon $p$-form theories · Introduction · 0.86
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Theories of this sort were first proposed back in 1974 by Horndeski [ref] , rediscovered in modified form in Refs. [ref] , and relatively recently emerged in Refs. [ref] in the context of the DGP model [ref] .
Superluminality in dilatationally invariant generalized Galileon theories · Introduction · 1.00
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