Questing mass dimension 1 spinor fields

Villalobos, C. H. Coronado; Silva, J. M. Hoff da; Rocha, Roldão da

doi:10.1140/epjc/s10052-015-3498-2

Cited by 31 publications

(20 citation statements)

References 30 publications

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“…Type-6 Lounesto spinor: This case is very similar to the type-4 one, asσ =ω = 0 andS = 0. The vector and pseudovector equations for the Heisenberg field are the same that in the type-4 spinor (28). Hence, if x = y thenJ = J/x = 0,K = K/x = 0.…”

Section: Heisenberg Spinor Fields Classificationmentioning

confidence: 89%

“…Hence, not all the classes with vanishing current density in Ref. [28] are necessary for the Heisenberg field classification.…”

Section: Discussionmentioning

confidence: 99%

“…The inequality J = 0 is valid for the entire classes in Lounesto's classification. Reference [28] constructed three more classes that are beyond Lounesto's classification, corresponding to J = 0, playing the role of ghost spinor fields. The Lounesto's classification splits the spinor fields into singular ones, with both vanishing σ and ω, and regular ones, where at least one between the scalar and pseudoscalar bilinear covariants are not equal to zero.…”

Section: Lounesto's Classification and Ramificationsmentioning

confidence: 99%

“…If x = y then we have three possibilities. If the condition J = y−x y+x K is satisfied, then it can be seen from (28), that J = 0 andK = 0. Hence, the Heisenberg spinor lies in the class (24e).…”

Section: Heisenberg Spinor Fields Classificationmentioning

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: Heisenberg Spinor Fields Classificationmentioning

confidence: 89%

“…Hence, not all the classes with vanishing current density in Ref. [28] are necessary for the Heisenberg field classification.…”

Section: Discussionmentioning

confidence: 99%

Section: Lounesto's Classification and Ramificationsmentioning

confidence: 99%

Section: Heisenberg Spinor Fields Classificationmentioning

confidence: 99%

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

2019

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“…Although we already know the general form of all kinds of spinors in Lounesto's classification [10], the dynamics for every spinors lacks, still. Mass dimension one fermions [11] can occupy both classes four and five of spinor fields.…”

Section: Introductionmentioning

confidence: 99%

Flag-dipole and flagpole spinor fluid flows in Kerr spacetimes

Rocha

Cavalcanti

2017

Phys. Atom. Nuclei

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Flagpole and flag-dipole spinors are particular classes of spinor fields that has been recently used in different branches of theoretical physics. In this paper, we study the possibility and consequences of these spinor fields to induce an underlying fluid flow structure in the background of Kerr spacetimes. We show that flag-dipole spinor fields are solutions of the equations of motion in this context. To our knowledge, this is the second time that this class of spinor field appears as a physical solution, the first one occurring as a solution of the Dirac equation in ESK gravities.

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General Dynamics of Spinors

Fabbri

2017

Adv. Appl. Clifford Algebras

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In this paper, we consider a general twisted-curved space-time hosting Dirac spinors and we take into account the Lorentz covariant polar decomposition of the Dirac spinor field: the corresponding decomposition of the Dirac spinor field equation leads to a set of field equations that are real and where spinorial components have disappeared while still maintaining Lorentz covariance. We will see that the Dirac spinor will contain two real scalar degrees of freedom, the module and the so-called Yvon-Takabayashi angle, and we will display their field equations. This will permit us to study the coupling of curvature and torsion respectively to the module and the YT angle. I. HISTORYThe Dirac equation is one of the most impressive successes in all of physics (and as far as we can tell, in all of human achievements): conceived from the purely theoretical (or in Dirac's thoughts, aesthetic) reason to be a covariant first-order derivative field equation, it turned out to account for spin and matter/antimatter duality.Such an extensively comprehensive description comes at the cost of a rather complicated formalism: as a start, spinors (in this paper we only consider Dirac spinors) are 4-dimensional columns of complex scalar fields, amounting to 8 real components. Moreover, the spinor formalism does not put in evidence the essence of any of the various components of a spinor field -So is there a way in which to write the spinor formalism so that all components display a clear meaning? Also, can we reduce the variety of the components by proving that some of them are not in fact true degrees of freedom? And if yes, then how many degrees of freedom are actually present in a spinor?These are all legitimate questions that researchers have been trying to answer, though not with the same impetus with which research has been done in more fashionable branches; still, some research has been done, and to our knowledge, the first to work on this problem were Jakobi and Lochak [1], followed after some time, but with a much richer research production, by Hestenes [2-4].The idea they had was to write the Dirac spinor field in the polar form: as a complex scalar can be written as the product of module times unitary phase, similarly the complex spinor should be writable as a column with four components, each of which being the product of a module times a unitary phase; while for scalars this construction is always trivial, spinors are defined in such a way that a spinorial transformation mixes the various components, and care must be exercised if we want the polar form to respect Lorentz symmetries. The works mentioned above do precisely this: they expound the spinor in a form that is polar while displaying a manifest Lorentz symmetry in its structure. As we will discuss later on, the polar form allows us to give a clear interpretation of the components of the spinor field and it shows which ones are artifacts and which ones are real degrees of freedom.On the basis of these results, Hestenes went further to discuss zitterbewegung effects...

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Questing mass dimension 1 spinor fields

Cited by 31 publications

References 30 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

Flag-dipole and flagpole spinor fluid flows in Kerr spacetimes

General Dynamics of Spinors

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