Gauge formulation of gravitation theories. I. The Poincaré, de Sitter, and conformal cases

Ivanov, E. A.; Niederle, J.

doi:10.1103/physrevd.25.976

Cited by 111 publications

(150 citation statements)

References 29 publications

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“…In 1980, Stelle and West [27] investigated the NLR induced by the spontaneous breakdown of SO (3,2). In 1982 Ivanov and Niederle considered nonlinear gauge theories of the Poincaré, de Sitter, conformal and special conformal groups [28,29]. In 1983, Ivanenko and Sardanashvily [30] considered gravity to be a spontaneously broken GL(4, R) gauge theory.…”

Section: While the Gauge Groups Involved In The Standardmentioning

confidence: 99%

Deriving the mass of particles from Extended Theories of Gravity in LHC era

Capozziello

Basini

2011

Eur. Phys. J. C

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We derive a geometrical approach to produce the mass of particles that could be suitably tested at LHC. Starting from a 5D unification scheme, we show that all the known interactions could be suitably deduced as an induced symmetry breaking of the non-unitary GL(4)-group of diffeomorphisms. The deformations inducing such a breaking act as vector bosons that, depending on the gravitational mass states, can assume the role of interaction bosons like gluons, electroweak bosons or photon. The further gravitational degrees of freedom, emerging from the reduction mechanism in 4D, eliminate the hierarchy problem since generate a cut-off comparable with electroweak one at TeV scales. In this "economic" scheme, gravity should induce the other interactions in a non-perturbative way.

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Section: While the Gauge Groups Involved In The Standardmentioning

confidence: 99%

Deriving the mass of particles from Extended Theories of Gravity in LHC era

Capozziello

Basini

2011

Eur. Phys. J. C

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“…Many authors, apparently unaware of the OP formalism in most (not all) cases, have imposed the symmetric gauge condition on the tetrad [Isham et al, 1971, Isham et al, 1973, Deser and van Nieuwenhuizen, 1974, 't Hooft and Veltman, 1974, Borisov and Ogievetskii, 1974, Cho and Freund, 1975, Hamamoto, 1978, Hamamoto, 1979, Boulware et al, 1979, Veltman, 1981, Ivanov and Niederle, 1982, Alvarez-Gaumé and Witten, 1984, Passarino, 1984, Fujikawa et al, 1985, Fujikawa et al, 1985, Choi et al, 1993, Aldrovandi et al, 1994, López-Pinto et al, 1995, Schücker, 2000, Tresguerres and Mielke, 2000, Bilyalov, 2002, Sardanashvily, 2002, Obukhov and Pereira, 2003, Vasiliev, 2003, Tiemblo and Tresguerres, 2004, Kirsch, 2005, Holstein, 2006, Leclerc, 2006a, Iochum and Schücker, 2006, Nibbelink et al, 2007. Those who were unaware of the OP spinor formalism and imposed the symetric gauge on the tetrad thus in effect partially reinvented the OP formalism.…”

Section: ]mentioning

confidence: 99%

The nontriviality of trivial general covariance: How electrons restrict ‘time’ coordinates, spinors (almost) fit into tensor calculus, and of a tetrad is surplus structure

Pitts

2012

Studies in History and Philosophy of Science Part B: Studies in

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It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus.On the other hand, the physics literature often claims that spinors as such cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is (nearly) Ockhamized, with most of the fluff removed. As developed * Forthcoming in Studies in History and Philosophy of Modern Physics 1 nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix diag(−1, 1, 1, 1), the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and values of the fields involved.Apart from coordinate order and the usual spinorial two-valuedness, (densitized) Ogievetsky-Polubarinov spinors form, with the (conformal part of the) met- The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited.

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“…Sitter group or the general linear group, GL(4, R), or the general affine group, GA(4, R) (see Trautman 1980b;Ivanov & Niederle 1982;Ivanenko & Sardanashvily 1983;Nounou 1995). Unlike the case of Poincaré group, which is intended to be a replacement of the Lorentz group, the GL(4, R) and GA(4, R) are generalizations.…”

Section: Gauge Theories Of Gravitymentioning

confidence: 99%

“…Ivanov &Niederle 1982 andMukunda 1989) in which attempts are made to treat the Poincaré group as an internal symmetry group when it is gauged --i.e. the elements of the group do not act on spacetime points at all.…”

Section: Gauge Theories Of Gravitymentioning

confidence: 99%

Gauge gravity and the unification of natural forces

Liu

2003

International Studies in the Philosophy of Science

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Gauge formulation of gravitation theories. I. The Poincaré, de Sitter, and conformal cases

Cited by 111 publications

References 29 publications

Deriving the mass of particles from Extended Theories of Gravity in LHC era

Deriving the mass of particles from Extended Theories of Gravity in LHC era

The nontriviality of trivial general covariance: How electrons restrict ‘time’ coordinates, spinors (almost) fit into tensor calculus, and of a tetrad is surplus structure

Gauge gravity and the unification of natural forces

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