Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance

Hehl, Friedrich W.; McCrea, J. D.; Mielke, Eckehard W.; Ne’eman, Yuval

doi:10.1016/0370-1573(94)00111-f

Cited by 1,426 publications

(1,922 citation statements)

References 447 publications

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“…Spinor fields in this approach are represented as "manifields" carrying infinitedimensional representations of the orthogonal subgroup (for comprehensive review of this approach see Ref. [13] and references therein). However in this way we lose the simple clear correspondence between vectors and spinors and should consider vector fields as infinite-dimensional as well.…”

Section: Jhep07(1998)016mentioning

confidence: 99%

“…Therefore nonmetricity W αβµ does not couple with spinor fields as far as one adopts minimal coupling of matter with gravity, and hence generalized spinors cannot form a hypothetical hypermomentum fluid (the source of nonmetricity) discussed in the literature (see e.g., [13]). Furthermore neither ReΦ µ nor N µ enter these equations.…”

Section: Physical Considerationsmentioning

confidence: 99%

“…However this is not a simple problem for, as is known [13], the torsion tensor has many varieties of Lagrangians, and it is very difficult to find out a natural Lagrangian for thẽ N λ [µν] . So we leave the study ofÑ λ[µν] for future investigations.…”

Section: Jhep07(1998)016mentioning

confidence: 99%

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Spinor-type objects in metric-affine space-time

Poberii¹

1998

J. High Energy Phys.

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A generalized spinor structure is constructed as a GL(2, C) principal fiber bundle over the metric-affine manifold. Relations between vectors and spinors are established explicitly through the generalized Pauli and Dirac matrices. An expression for generalized spinor connection is obtained. The Dirac equation in metric-affine space-time is written in the form representing an interaction of spinors with nonmetricity explicitly. A possible physical meaning of nonmetrical objects is discussed in brief.

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Section: Jhep07(1998)016mentioning

confidence: 99%

Section: Physical Considerationsmentioning

confidence: 99%

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Spinor-type objects in metric-affine space-time

Poberii¹

1998

J. High Energy Phys.

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“…This approach is known as teleparallel theory (TT) [26][27][28][29], which is demonstrably equivalent to GR. In order to describe not only the gravitational interaction, but also the accelerated expansion of our universe, Ferraro and Fiorini [30] proposed a possible generalization of the TT, which became known as f (T ) gravity , which up to now has provided good results in both cosmology and local phenomena of gravitation.…”

Section: Introductionmentioning

confidence: 99%

Generalized teleparallel theory

Ednaldo

Rodrigues

2016

Eur. Phys. J. C

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We construct a theory in which the gravitational interaction is described only by torsion, but that generalizes the teleparallel theory still keeping the invariance of local Lorentz transformations in one particular case. We show that our theory falls, in a certain limit of a real parameter, under f (R) gravity or, in another limit of the same real parameter, under modified f (T ) gravity; on interpolating between these two theories it still can fall under several other theories. We explicitly show the equivalence with f (R) gravity for the cases of a Friedmann-Lemaître-Robertson-Walker flat metric for diagonal tetrads, and a metric with spherical symmetry for diagonal and non-diagonal tetrads. We study four applications, one in the reconstruction of the de Sitter universe cosmological model, for obtaining a static spherically symmetric solution of de Sitter type for a perfect fluid, for evolution of the state parameter ω DE , and for the thermodynamics of the apparent horizon.

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“…Various types of Finsler-like structures can be parametrized by generic off-diagonal metrics, which cannot be diagonalized by coordinate transforms but only by anholonomic maps with associated nonlinear connection (in brief, N-connection). Such structures may be defined as exact solutions of gravitational field equations in the Einstein gravity and its generalizations [75,79,80,94,95,96,97,98,99,100,102,103,104,105,109,110,111], for instance, in the metric-affine [19,23,56] Riemann-Cartan gravity [24,25]. Finsler-like configurations are considered in locally anisotropic thermodynamics, kinetics, related stochastic processes [85,96,107,108], and (super-) string theory [84,87,90,91,92].…”

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confidence: 99%

Nonlinear connections and spinor geometry

Vacaru¹,

Vicol

2004

International Journal of Mathematics and Mathematical Sciences

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We present an introduction to the geometry of higher-order vector and covector bundles (including higher-order generalizations of the Finsler geometry and Kaluza-Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for application of Finsler-like geometries in modern string and gravity theory, noncommutative geometry and noncommutative field theory, and gravity.2000 Mathematics Subject Classification: 15A66, 58B20, 53C60, 83C60, 83E15.1. Introduction. Nowadays, interest has been established in non-Riemannian geometries derived in the low-energy string theory [18,64,65], noncommutative geometry [1,3,8,12,15,22,32,34,53,55,67,109,111,112], and quantum groups [33,35,36,37]. Various types of Finsler-like structures can be parametrized by generic off-diagonal metrics, which cannot be diagonalized by coordinate transforms but only by anholonomic maps with associated nonlinear connection (in brief, N-connection). Such structures may be defined as exact solutions of gravitational field equations in the Einstein gravity and its generalizations [75,79,80,94,95,96,97,98,99,100,102,103,104,105,109,110,111], for instance, in the metric-affine [19,23,56] Riemann-Cartan gravity [24,25]. Finsler-like configurations are considered in locally anisotropic thermodynamics, kinetics, related stochastic processes [85,96,107,108], and (super-) string theory [84,87,90,91,92].The following natural step in these lines is to elucidate the theory of spinors in effectively derived Finsler geometries and to relate this formalism of Clifford structures to noncommutative Finsler geometry. It should be noted that the rigorous definition of spinors for Finsler spaces and generalizations was not a trivial task because (on such spaces) there are no defined even local groups of automorphisms. The problem was solved in [82,83,88,89,93] by adapting the geometric constructions with respect to anholonomic frames with associated N-connection structure. The aim of this work is to outline the geometry of generalized Finsler spinors in a form more oriented to applications in modern mathematical physics.We start with some historical remarks: the spinors studied by mathematicians and physicists are connected with the general theory of Clifford spaces introduced in 1876 [14]. The theory of spinors and Clifford algebras play a major role in contemporary physics and mathematics. The spinors were discovered by Èlie Cartan in 1913 in 1190 S. I. VACARU AND N. A. VICOL mathematical form in his researches on representation group theory [10,11]; he showed that spinors furnish a linear representation of the groups of rotations of a space of arbitrary dimensions. The physicists Pauli [60] and Dirac [20] (in 1927, resp., for the three-dimensional and four-dimensional space-times) introduced spinors for the representation of the wave functions. In general relativity theory spinors and the Dirac equat...

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Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance

Cited by 1,426 publications

References 447 publications

Spinor-type objects in metric-affine space-time

Spinor-type objects in metric-affine space-time

Generalized teleparallel theory

Nonlinear connections and spinor geometry

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