World spinors—Construction and some applications

Ne’eman, Yuval; Šijački, Djordje

doi:10.1007/bf02551436

Cited by 7 publications

(5 citation statements)

References 26 publications

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“…Ψ of GL(n, R). It has been suggested [19,25,38,39] that such a spinor could be described by an affine extension of the Dirac equation which would follow from the action…”

Section: A Breaking Of Gl(n R) and Hybrid Inflationmentioning

confidence: 99%

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Higgs mechanism for gravity

Kirsch

2005

Phys. Rev. D

127

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In this paper we elaborate on the idea of an emergent spacetime which arises due to the dynamical breaking of diffeomorphism invariance in the early universe. In preparation for an explicit symmetry breaking scenario, we consider nonlinear realizations of the group of analytical diffeomorphisms which provide a unified description of spacetime structures. We find that gravitational fields, such as the affine connection, metric and coordinates, can all be interpreted as Goldstone fields of the diffeomorphism group. We then construct a Higgs mechanism for gravity in which an affine spacetime evolves into a Riemannian one by the condensation of a metric. The symmetry breaking potential is identical to that of hybrid inflation but with the non-inflaton scalar extended to a symmetric second rank tensor. This tensor is required for the realization of the metric as a Higgs field. We finally comment on the role of Goldstone coordinates as a dynamical fluid of reference.

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“…Ψ of GL(n, R). It has been suggested [19,25,38,39] that such a spinor could be described by an affine extension of the Dirac equation which would follow from the action…”

Section: A Breaking Of Gl(n R) and Hybrid Inflationmentioning

confidence: 99%

“…As an aside we remark that matter in an affine spacetime is described by a spinorial infinite-component field Ψ of GL(n, R). It has been suggested [19,25,38,39] that such a spinor could be described by an affine extension of the Dirac equation which would follow from the action…”

Section: A Breaking Of Gl(n R) and Hybrid Inflationmentioning

confidence: 99%

Higgs mechanism for gravity

Kirsch

2005

Phys. Rev. D

127

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“…Nevertheless, it is worth stressing that infinite representations of such a group do exist, as shown in [15,16] and the references therein. Finite spinors can introduced either by making use of the nonlinear representations of the double covering of the general-coordinate-transformation group, which are linear when restricted to the Poincaré subgroup, or by introducing a bundle of cotangent frames and defining in this space the action of a physically-distnct Lorentz group.…”

Section: Introductionmentioning

confidence: 99%

“…In the second case, after generalizing the Lorentz group, infinite-dimensional linear spinor representations or finitedimensional non-linear spinor representations can be found. In [16], infinite-component spinor and tensor fields (so-called manifields) are introduced: these manifields are are then lifted to the proper corresponding representation via the introduction of infinite-component frame-fields.…”

Section: Introductionmentioning

confidence: 99%

Novel analysis of spinor interactions and non-Riemannian geometry

2013

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A novel analysis of the gauge theory of the local Lorentz group is implemented both in flat and in curved space-time, and the resulting dynamics is analyzed in view of the geometrical interpretation of the gauge potential. The Yang-Mills picture of local Lorentz transformations is first approached in a second-order formalism. For the Lagrangian approach to reproduce the second Cartan structure equation as soon as the Lorentz gauge connections are identified with the contortion tensor, an interaction term between the Lorentz gauge fields and the spin connections has to be postulated. The full picture involving gravity, torsion and spinors is described by a coupled set of field equations, which allows one to interpret both gravitational spin connections and matter spin density as the source term for the Yang-Mills equations. The contortion tensor acquires a propagating character, because of its non-Abelian feature, and the pure contact interaction is restored in the limit of vanishing Lorentz connections.[PACS: 02.40.Hw, 04.62.+v]

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“…Affine-invariant extensions of the Dirac equation have been studied in [9,1,5,15]. Mickelsson [9] has constructed a GL(4, R) covariant extension of the Dirac equation.…”

Section: Introductionmentioning

confidence: 99%

From Poincar$eacute$ to affine invariance: how does the Dirac equation generalize?

Kirsch¹,

Šijački²

2002

Class. Quantum Grav.

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A generalization of the Dirac equation to the case of affine symmetry, with SL(4, R) replacing SO(1, 3), is considered. A detailed analysis of a Dirac-type Poincaré-covariant equation for any spin j is carried out, and the related general interlocking scheme fulfilling all physical requirements is established. Embedding of the corresponding Lorentz fields into infinite-component SL(4, R) fermionic fields, the constraints on the SL(4, R) vector-operator generalizing Dirac's γ matrices, as well as the minimal coupling to (Metric-)Affine gravity are studied. Finally, a symmetry breaking scenario for SA(4, R) is presented which preserves the Poincaré symmetry.

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World spinors—Construction and some applications

Cited by 7 publications

References 26 publications

Higgs mechanism for gravity

Higgs mechanism for gravity

Novel analysis of spinor interactions and non-Riemannian geometry

From Poincar$eacute$ to affine invariance: how does the Dirac equation generalize?

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