scholarly journals Spin-Valued Four Bosons Electrodynamics

2021 ◽  
Vol 19 ◽  
pp. 93-133
Author(s):  
R. Doria ◽  
I. Soares
Keyword(s):  
Lie Algebra ◽  
Electric Charge ◽  
Lorentz Group ◽  
Vector Fields ◽  
Magnetic Moments ◽  
Equations Of Motion ◽  
Spin Coupling ◽  
Abelian Gauge ◽  
Spin Effects ◽  
Massive Photon

Electromagnetism is based on electric charge and spin. The study here corresponds to understand on spin effects at a vectorial electrodynamics. Its scenario is a non-linear abelian electromagnetism where the electric charge is transmitted through a four bosons quadruplet, constituted by the usual photon, massive photon and charged massive photons. These four bosons intermediate the charge exchange ΔQ = 0, ±1.The spin is introduced at first principles. A spintronics Lagrangian for four vector fields is performed. Considering that spin is a space-time physical entity derived from Lorentz Group, these vector fields are associated to Lorentz Group, as Lie algebra valued. Similarly to non-abelian gauge theories where Aμ≡ Aμ,ata, one introduces the relationship Aμ≡ Aμ,κλΣκλ where (Σκλ)αβ is the Lorentz Group generator. Thus, based on three fundamentals which are light invariance, electric charge conservation law and vector fields Lie algebra valued through Lorentz Group generators, one derives a spin-valued four vectorial electrodynamics. It is given by the fields quadruplet Aμ1 ≡ {Aμ, Uμ, Vμ±}  where Aμ means the usual photon, Uμ a massive photon and Vμ± massive charged photons. Two novelties appear. The first one is that, new terms are developed into usual four bosons electromagnetism. They contribute to Lagrangian, equations of motion, Noether theorem. The second one is that the equations of motion derive a renormalizable spin coupling with the electric and magnetic fields.There is a spin-1 electrodynamics to be investigated. A neutral electromagnetism is mandatory to be analyzed. Something beyond dipole, quadrupole and so on. Understand the role of spin in the electrical and magnetic properties of particles. A spin vectorial expression S-->  is obtained. It adds EM interactions not depending on electric charge and with spin interactions through electric dipole and magnetic moments.

Four Bosons Electromagnetism

2015 ◽  
Vol 10 (1) ◽  
pp. 2610-2640
Author(s):  
Renato Doria ◽  
J. Chauca ◽  
I. Soares
Keyword(s):  
Variational Principle ◽  
Gauge Symmetry ◽  
Electric Charge ◽  
Navier Stokes ◽  
Gauge Parameter ◽  
Physical Situation ◽  
Abelian Gauge ◽  
Charge Conservation ◽  
Massive Photon ◽  
Vector Bosons

Based on light invariance and electric conservation a four bosons electromagnetism is proposed. It enlarges the electric charge conservation beyond displacement current and Dirac charge to a new physical situation where the electromagnetic phenomena is mediated by the usual photon plus a massive photon and two additional charged vector bosons.Considering the enlarged abelian gauge symmetry U(1) SO(2) transforming under a same gauge parameter a non-linear electromagnetism involving four bosons is introduced. It deploys a Lagrangian containing massless, massive and charged elds with three and four vector bosons interactions. The corresponding Noether's relations and classical equations of motion are studied. They provide a whole dynamics involving granular, collective terms through antisymmetric and symmetric sectors. It develops a new photon equation which extends the Maxwell's one. Self interacting photons are obtained.A four boson electromagnetic ux is derived. It expresses an electromagnetism transfering 4Q = 0 and j4Qj = 1, not more limited to just a massless photon. There is a new electromagnetic owing to be understood, where aside of electric charge conservation, it appears a neutral electromagnetism. There are six neutral electromagnetic charges beyond electric charge as consequences from non-linearity. Two are derived from the second Noether identity and four from variational continuity equations. An electromagnetic ux being conducted by a whole physics is generated. Based on elds set, it develops a determinism under the meaning of directive and circumstance. Interpreting that, light invariance concises the photon as directive, the photon becomes a whole maker. It assumes the symmetry command which will control the conservations laws and opportunities. Consequently, one combines the symmetry equation derived fromNoether theorem with the four equations derived from variational principle, and an effective photon equation is obtained. A kind of Navier-Stokes electromagnetic ow is derived. It yields a four bosons electromagnetism preserving electric charge conservation plus introducting the meaning of chance through symmetry management.

A note on the algebra of Poisson brackets

1984 ◽  
Vol 96 (1) ◽  
pp. 45-60 ◽  
Author(s):  
C. J. Atkin
Keyword(s):  
Poisson Bracket ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Symplectic Manifold ◽  
Vector Fields ◽  
Poisson Brackets ◽  
Infinite Dimensional

In a long sequence of notes in the Comptes Rendus and elsewhere, and in the papers [1], [2], [3], [6], [7], Lichnerowicz and his collaborators have studied the ‘classical infinite-dimensional Lie algebras’, their derivations, automorphisms, co-homology, and other properties. The most familiar of these algebras is the Lie algebra of C∞ vector fields on a C∞ manifold. Another is the Lie algebra of ‘Poisson brackets’, that is, of C∞ functions on a C∞ symplectic manifold, with the Poisson bracket as composition; some questions concerning this algebra are of considerable interest in the theory of quantization – see, for instance, [2] and [3].

scholarly journals Representations of the Lie algebra of vector fields on a sphere

2019 ◽  
Vol 223 (8) ◽  
pp. 3581-3593 ◽  
Author(s):  
Yuly Billig ◽  
Jonathan Nilsson
Keyword(s):  
Lie Algebra ◽  
Vector Fields

scholarly journals Origin of the Low Magnetic Moment in Fe2AlTi: An Ab Initio Study

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1732 ◽  
Author(s):  
Martin Friák ◽  
Anton Slávik ◽  
Ivana Miháliková ◽  
David Holec ◽  
Monika Všianská ◽  
...  
Keyword(s):  
Ab Initio ◽  
Magnetic Moment ◽  
Energy Surface ◽  
Magnetic Moments ◽  
Local Magnetic Moment ◽  
Spin Configuration ◽  
Spin Effects ◽  
Order Of Magnitude ◽  
Huge Impact ◽  
Insight Into

The intermetallic compound Fe 2 AlTi (alternatively Fe 2 TiAl) is an important phase in the ternary Fe-Al-Ti phase diagram. Previous theoretical studies showed a large discrepancy of approximately an order of magnitude between the ab initio computed magnetic moments and the experimentally measured ones. To unravel the source of this discrepancy, we analyze how various mechanisms present in realistic materials such as residual strain effects or deviations from stoichiometry affect magnetism. Since in spin-unconstrained calculations the system always evolves to the spin configuration which represents a local or global minimum in the total energy surface, finite temperature spin effects are not well described. We therefore turn the investigation around and use constrained spin calculations, fixing the global magnetic moment. This approach provides direct insight into local and global energy minima (reflecting metastable and stable spin phases) as well as the curvature of the energy surface, which correlates with the magnetic entropy and thus the magnetic configuration space accessible at finite temperatures. Based on this approach, we show that deviations from stoichiometry have a huge impact on the local magnetic moment and can explain the experimentally observed low magnetic moments.

scholarly journals Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1354 ◽  
Author(s):  
Hassan Almusawa ◽  
Ryad Ghanam ◽  
Gerard Thompson
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Fields ◽  
Solvable Lie Groups ◽  
Related System ◽  
Geodesic Equations ◽  
Solvable Lie Algebras ◽  
Symmetry Algebras

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A 5 , 7 a b c to A 18 a . For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

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