Cosmology of a Heisenberg fluid

Joffily, S.; Novello, M.

doi:10.1007/s10714-016-2145-z

Cited by 4 publications

(5 citation statements)

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“…Tables 2 and 3 would make possible to seek for solutions of the Dirac equation for other classes of Lounesto spinor fields. As a prototypical Heisenberg dynamics was employed to study anisotropic cosmological models [23], one may then explore this kind of dynamics for other types of Heisenberg spinor fields in the context of the minimal geometric deformation [32].…”

Section: Discussionmentioning

confidence: 99%

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The Heisenberg spinor field classification and its interplay with the Lounesto’s classification

2019

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Dirac linear spinor fields were obtained from non-linear Heisenberg spinors, in the literature. Here we extend that idea by considering not only Dirac spinor fields but spinor fields in any of the Lounesto's classes. When one starts considering all these classes of fields, the question of providing a classification for the Heisenberg spinor naturally arises. In this work the classification of Heisenberg spinor fields is derived and scrutinized, in its interplay with the Lounesto's spinor field classification.

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Section: Discussionmentioning

confidence: 99%

“…Dirac spinor fields were described by a non-linear mixture of Heisenberg spinors fields [22], to show that neutrinos are quantum field states of Heisenberg spinor fields. Besides, Heisenberg dynamics was employed to study anisotropic cosmological models, generated by a non-linear fermionic ultra-relativistic fluid [23].…”

Section: Introductionmentioning

confidence: 99%

The Heisenberg spinor field classification and its interplay with the Lounesto’s classification

2019

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“…, which means, in particular, that (b − b) = 0. In fact, by (17), otherwise, we would end up with K µ → ∞, leading to an unphysical result. Now, in reference [2], it is claimed that J µ and K µ constitute a basis for vectors constructed by the derivative ∂ µ operating on functionals of Ψ H , and one has the following equations (which are valid for every µ):…”

Section: On the Dirac Dual Bilinear Covariants And Lounesto Classific...mentioning

confidence: 99%

“…The non-linear Heisenberg equation of motion is easily obtained by varying the action with respect to the spinor field, constructed by [16,17]…”

Section: B a Short Overview On The Non-linear Heisenberg Theory Formmentioning

confidence: 99%

“…With regard to direct physical applications, this work provides a homotopical method of construction of any possible spinor field allowed in the Spinor Theory of Gravity (STG), which is a theory of gravitation built via a class of solutions of the linearized Einstein equations of General Relativity constructed from RIM-spinors [17,19], i.e., a gravitation theory with RIM-spinors playing a fundamental role. Moreover, since bilinear covariants are associated with physical observables, we developed a way to easy verify the possible couplings of a particle associated to a given spinor in this theory, by means of their coefficients in the RIM-decomposition.…”

Section: Final Remarksmentioning

confidence: 99%

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The restricted Inomata-McKinley spinor-plane, homotopic deformations and the Lounesto classification

Beghetto

Rogerio

Villalobos

2019

Journal of Mathematical Physics

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We define a two-dimensional space called the spinor-plane, where all spinors that can be decomposed in terms of Restricted Inomata-McKinley (RIM) spinors reside, and describe some of its properties. Some interesting results concerning the construction of RIM-decomposable spinors emerge when we look at them by means of their spinor-plane representations. We show that, in particular, this space accomodates a bijective linear map between mass-dimension-one and Dirac spinor fields. As a highlight result, the spinor-plane enables us to construct homotopic equivalence relations, revealing a new point of view that can help to give one more step towards the understanding of the spinor theory. In the end, we develop a simple method that provides the categorization of RIM-decomposable spinors in the Lounesto classification, working by means of spinor-plane coordinates, which avoids the often hard work of analising the bilinear covariant structures one by one.PACS numbers: 02.40.Re, 03.50.-z, 03.70.+k * Electronic address: dbeghetto@feg.unesp.br † Electronic address: rodolforogerio@feg.unesp.br ‡ Electronic address: ccoronado@id.uff.br 1 In this work, what we call by a manifold with underlying trivial topology is a manifold M that has a trivial fundamental group π 1 (M ) = 0. Otherwise, the manifold M will be said to have a non-trivial topology. 2 We will use "MDO" to call these spinor fields.

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The (restricted) Inomata-McKinley spinor representation and the underlying topology

Beghetto

Silva

2017

EPL

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The so called Inomata-McKinley spinors are a particular solution of the non-linear Heisenberg equation. In fact, free linear massive (or mass-less) Dirac fields are well known to be represented as a combination of Inomata-McKinley spinors. More recently, a subclass of Inomata-McKinley spinors were used to describe neutrino physics. In this paper we show that Dirac spinors undergoing this restricted Inomata-McKinley decomposition are necessarily of the first type, according to the Lounesto classification. Moreover, we also show that this type one subclass spinors has not an exotic counterpart. Finally, implications of these results are discussed, regarding the understanding of the spacetime background topology.

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Cosmology of a Heisenberg fluid

Abstract: We consider a scenario in which the global geometry of the universe is driven by non-linear fermions obeying Heisenberg dynamics.

Cited by 4 publications

References 10 publications

The Heisenberg spinor field classification and its interplay with the Lounesto’s classification

The Heisenberg spinor field classification and its interplay with the Lounesto’s classification

The restricted Inomata-McKinley spinor-plane, homotopic deformations and the Lounesto classification

The (restricted) Inomata-McKinley spinor representation and the underlying topology

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