scholarly journals THE QUADRATIC SPINOR LAGRANGIAN, AXIAL TORSION CURRENT AND GENERALIZATIONS

2007 ◽  
Vol 16 (10) ◽  
pp. 1653-1667 ◽  
Author(s):  
R. DA ROCHA ◽  
J. G. PEREIRA
Keyword(s):  
Dirac Equation ◽  
Current Density ◽  
Boundary Component ◽  
Spinor Field ◽  
Hamiltonian Formalism ◽  
Gravity Theory ◽  
Boundary Term ◽  
Dirac Spinor ◽  
Axial Torsion ◽  
Spinor Fields

We show that the Einstein–Hilbert, the Einstein–Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein–Hilbert, Einstein–Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field — Weyl, Majorana, flagpole, or flag-dipole spinor fields — yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

scholarly journals Fermion localization in braneworld teleparallel f(T, B) gravity

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
A. R. P. Moreira ◽  
J. E. G. Silva ◽  
C. A. S. Almeida
Keyword(s):  
Scalar Field ◽  
Yukawa Coupling ◽  
Spinor Field ◽  
Quantum Potential ◽  
Boundary Term ◽  
Dirac Spinor ◽  
Kaluza Klein ◽  
Fermion Localization

AbstractWe study a spin 1/2 fermion in a thick braneworld in the context of teleparallel f(T, B) gravity. Here, f(T, B) is such that $$f_1(T,B)=T+k_1B^{n_1}$$ f 1 ( T , B ) = T + k 1 B n 1 and $$f_2(T,B)=B+k_2T^{n_2}$$ f 2 ( T , B ) = B + k 2 T n 2 , where $$n_{1,2}$$ n 1 , 2 and $$k_{1,2}$$ k 1 , 2 are parameters that control the influence of torsion and the boundary term. We assume Yukawa coupling, where one scalar field is coupled to a Dirac spinor field. We show how the $$n_{1,2}$$ n 1 , 2 and $$k_{1,2}$$ k 1 , 2 parameters control the width of the massless Kaluza–Klein mode, the breadth of non-normalized massive fermionic modes and the properties of the analogue quantum-potential near the origin.

scholarly journals ELKO SPINOR FIELDS: LAGRANGIANS FOR GRAVITY DERIVED FROM SUPERGRAVITY

2009 ◽  
Vol 06 (03) ◽  
pp. 461-477 ◽  
Author(s):  
ROLDÃO DA ROCHA ◽  
J. M. HOFF DA SILVA
Keyword(s):  
Spinor Field ◽  
Sufficient Conditions ◽  
Dirac Spinor ◽  
Weyl Spinor ◽  
Conjugation Operator ◽  
Spinor Fields ◽  
Mass Dimension ◽  
Majorana Spinor ◽  
Dimension One ◽  
Elko Spinor Fields

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong — together with Majorana spinor fields — to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein–Hilbert, the Einstein–Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that — in particular — the Einstein–Hilbert, Einstein–Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator — leading ELKO Lagrangian into the Dirac Lagrangian — is also pointed out, together with its relationship to the instanton Hopf fibration.

Gravitational interactions in the Dirac spinor fields and possible structure of local space-time of fermions

2021 ◽  
pp. 129-135
Author(s):  
V.G. Krechet ◽  
◽  
V.B. Oshurko ◽  
A.E. Baidin ◽  
◽  
...  
Keyword(s):  
General Relativity ◽  
Magnetic Moment ◽  
Spinor Field ◽  
Space Time ◽  
Spin Interaction ◽  
Internal Space ◽  
Dirac Spinor ◽  
Geometric Properties ◽  
Spinor Fields ◽  
Local Space

In the framework of general relativity, possible effects of the gravitational interactions in the Dirac spinor field are considered. It is shown that these interactions manifest locally as contact spin-spin interaction of the gravitational and spinor fields. This interaction leads to the classical rotation of particles with spin ħ /2. As a result, it leads to appearance of local internal space-time with specific geometric properties for each particle. New effect of an increase of the mass of spinor particles due to this interaction is found. Also, an explanation of the existence of a magnetic moment in Dirac spinor particles as a result of a local electro-spin-spin interaction has been proposed.

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

scholarly journals Geometry, Zitterbewegung, quantization

2019 ◽  
Vol 16 (09) ◽  
pp. 1950146 ◽  
Author(s):  
Luca Fabbri
Keyword(s):  
Explicit Form ◽  
Dirac Spinor ◽  
Internal Dynamics ◽  
Spinor Fields ◽  
Field Quantization ◽  
The Way

In the most general geometric background, we study the Dirac spinor fields with particular emphasis given to the explicit form of their gauge momentum and the way in which this can be inverted so as to give the expression of the corresponding velocity; we study how Zitterbewegung affects the motion of particles, focusing on the internal dynamics involving the chiral parts; we discuss the connections to field quantization, sketching in what way anomalous terms may be gotten eventually.

On the Functional Definition and Calculation of Global Observables in Nonlinear Spinor Field Quantum Theory

1972 ◽  
Vol 27 (7) ◽  
pp. 1058-1072
Author(s):  
H Stumpf
Keyword(s):  
Quantum Theory ◽  
Spinor Field ◽  
Free Field ◽  
Functional Space ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Spinor Fields

Abstract Nonlinear spinor theory contains unobservable field operators which cannot be identified with free field operators. Therefore for the comparson with experiment a theory of observables for nonlinear spinor fields is required. This theory is developed for global observables by means of a map into functional space, and leads to a functional quantum theory of nonlinear spinor fields

Quantum numbers for Dirac spinor fields on a curved space-time

1979 ◽  
Vol 20 (2) ◽  
pp. 409-413 ◽  
Author(s):  
R. G. McLenaghan ◽  
Ph. Spindel
Keyword(s):  
Space Time ◽  
Dirac Spinor ◽  
Curved Space ◽  
Spinor Fields ◽  
Quantum Numbers

Renormalized quantum stress–energy tensor for massive spinor fields around global monopoles

2020 ◽  
Vol 35 (11) ◽  
pp. 2050077
Author(s):  
Owen Pavel Fernández Piedra
Keyword(s):  
Spinor Field ◽  
Energy Conditions ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Spinor Fields ◽  
Characteristic Radius ◽  
Stress Energy ◽  
Massive Spinor ◽  
Global Monopoles ◽  
Tensor Formula

The renormalized quantum stress–energy tensor [Formula: see text] for a massive spinor field around global monopoles is constructed within the framework of Schwinger–DeWitt approximation, valid whenever the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry. The results obtained show that the quantum massive spinor field in the global monopole spacetime violates all the pointwise energy conditions.

scholarly journals FROM DIRAC ACTION TO ELKO ACTION

2009 ◽  
Vol 24 (16n17) ◽  
pp. 3227-3242 ◽  
Author(s):  
J. M. HOFF DA SILVA ◽  
ROLDÃO DA ROCHA
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Natural Extension ◽  
Dirac Spinor ◽  
Spinor Fields ◽  
The Standard Model ◽  
Mass Dimension ◽  
Fermionic Fields ◽  
Elko Spinor Fields ◽  
First Time

A fundamental action, representing a mass dimension-transmuting operator between Dirac and ELKO spinor fields, is performed on the Dirac Lagrangian, in order to lead it into the ELKO Lagrangian. Such a dynamical transformation can be seen as a natural extension of the Standard Model that incorporates dark matter fields. The action of the mass dimension-transmuting operator on a Dirac spinor field, that defines and introduces such a mapping, is shown to be a composition of the Dirac operator and the nonunitary transformation that maps Dirac spinor fields into ELKO spinor fields, defined in J. Math. Phys.48, 123517 (2007). This paper gives allowance for ELKO, as a candidate to describe dark matter, to be incorporated in the Standard Model. It is intended to present for the first time, up to our knowledge, the dynamical character of a mapping between Dirac and ELKO spinor fields, transmuting the mass dimension of spin one-half fermionic fields from 3/2 to 1 and from 1 to 3/2.

POLYNOMIAL SOLUTIONS OF HEUN EQUATION DESCRIBING FERMIONS IN GRAPHENE

2013 ◽  
Vol 27 (32) ◽  
pp. 1350190 ◽  
Author(s):  
MARINA-AURA DARIESCU ◽  
CIPRIAN DARIESCU
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Current Density ◽  
Hermite Polynomials ◽  
Heun Equation ◽  
Conserved Current ◽  
Familiar Form ◽  
The Magnetic Field ◽  
Massless Fermions

The wavefunctions describing the massless fermions evolving in a static magnetic field orthogonal to a radially planar electric field are obtained, as solutions to Dirac equation. In the case of the magnetic field alone, the corresponding HeunB confluent functions turn into the usual Hermite polynomials and the energy spectrum has the familiar form which has been reported for graphene samples. Within a more involved analysis with both electric and magnetic orthogonal static fields, we compute the conserved current density component and the quantized off-diagonal conductivity.

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