Gauge Invariance of Sedeonic Equations for Massive and Massless Fields

Миронов, В. Л.; Mironov, Sergey V.

doi:10.1007/s10773-016-2941-y

Cited by 9 publications

(5 citation statements)

References 19 publications

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“…For a certainly not complete list see e.g. [1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27]. These works don't necessarily assume locally-Lorentzian spacetime as foundational.…”

Section: Contextmentioning

confidence: 99%

Phenomenology from Dirac Equation with Euclidean-Minkowskian “Gravity Phase”

Köplinger

2023

Int J Theor Phys

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Over the past decades, many authors advertised models on complexified spacetime algebras for use in describing gravity. This work aims at providing phenomenological support to such claims, by introducing a one-parameter real phase α to the conventional Dirac equation with 1 r -type potential. This phase allows to transition between Euclidean (α = 0, ±π, ±2π, . . .) and Minkowskian (α = ± π 2 , ± 3π 2 , . . .) geometry, as two distinct cases that one may expect from some complexified spacetime. The configuration space is modeled on 4 × 4 matrix algebra over the bicomplex numbers, C ⊕ C. Spin-1 2 Coulomb scattering (Rutherford scattering) in Born approximation is then executed. All calculations are done "from scratch", as they could have been done some 85 years ago. By removing elegance from field theory that has since become customary, this paper aims at remaining as generally applicable as possible, for a wide range of candidate models that contain such a phase α in one way or another. Results for backscattering and cross section at high energies are compared with results from General Relativity calculations. Effects on intergalactic gas distribution and momentum transfer from scattering high-energy leptons are sketched.

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Section: Contextmentioning

confidence: 99%

Phenomenology from Dirac Equation with Euclidean-Minkowskian “Gravity Phase”

Köplinger

2023

Int J Theor Phys

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“…which is the analog of Pointing theorem in electrodynamics [21,32]. The first-order wave equation (71) has the solution in the form of plane wave:…”

Section: Maxwell Equations For Ideal Fluidmentioning

confidence: 99%

“…Recently we proposed the associative algebra of sixteen-component sedeons, which takes into account the properties of physical values with respect to the space-time inversion and realizes the scalar-vector representation of Poincare group [29,30]. This formalism was successfully applied for the description of classical and quantum fields [31][32][33]. In particular, we have demonstrated the possibility to formulate Maxwell-like equations for the fields with nonzero mass of quantum [31,32] and the unification of equations for electromagnetic field and weak gravity in the frames of gravitoelectromagnetism theory [33].…”

Section: Introductionmentioning

confidence: 99%

“…This formalism was successfully applied for the description of classical and quantum fields [31][32][33]. In particular, we have demonstrated the possibility to formulate Maxwell-like equations for the fields with nonzero mass of quantum [31,32] and the unification of equations for electromagnetic field and weak gravity in the frames of gravitoelectromagnetism theory [33]. In present paper we develop the description of ideal fluid using the sedeonic first-order wave equation for the fluid potentials.…”

Section: Introductionmentioning

confidence: 99%

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Sedeonic equations of ideal fluid

Миронов

Mironov

2017

Journal of Mathematical Physics

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In the present paper we propose the generalized equations for ideal fluid based on space-time algebra of sixteen-component sedeons. It is shown that the dynamics of isentropic fluid can be described by sedeonic first-order wave equation for fluid potentials. The key features of the proposed formalism are illustrated on the problem of the sound waves propagation. We consider the plane wave solution of linearized sedeonic wave equation and derive the second-order relations for the sound potentials analogues to the Pointing theorem in electrodynamics. The generalization of proposed sedeonic equations for the description of viscous fluid is also discussed.

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“…Making use of the sedenions, the authors [58] demonstrated some fundamental aspects of massive field's theory, including the gauge invariance, charge conservation, Poynting's theorem, potential of a stationary scalar point source, plane wave solution, and interactions between point sources. On the basis of the sedenionic space-time operators and sedenionic wavefunctions, the authors [59] discussed the gauge invariance of generalized second-order and first-order wave equations for massive and massless fields. Demir et al [60] presented the conic sedenionic formulation for the unification of generalized field equations of dyons (electromagnetic theory) and gravito-dyons (linear gravity).…”

Section: Introductionmentioning

confidence: 99%

Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

Weng¹

2017

Advances in Mathematical Physics

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The paper aims to apply the complex-sedenions to explore the wavefunctions and field equations of non-Abelian gauge fields, considering the spatial dimensions of a unit vector as the color degrees of freedom in the complex-quaternion wavefunctions, exploring the physical properties of the color confinement essentially. J. C. Maxwell was the first to employ the quaternions to study the physical properties of electromagnetic fields. His method inspires some subsequent scholars to introduce the quaternions, octonions, and sedenions to research the electromagnetic field, gravitational field, nuclear field, quantum mechanics, and gauge field. The application of complex-sedenions is capable of depicting not only the field equations of the classical mechanics on the macroscopic scale, but also the field equations of the quantum mechanics on the microscopic scale. The latter can be degenerated into the Dirac equation and Yang-Mills equation. In contrast to the complex-number wavefunction, the wavefunction in the complex-quaternion space possesses three new degrees of freedom, that is, three color degrees of freedom. One complex-quaternion wavefunction is equivalent to three conventional wavefunctions with the complex-numbers. It means that the three spatial dimensions of unit vector in the complex-quaternion wavefunction can be considered as the 'three colors', naturally the color confinement will be effective. In other words, in the complex-quaternion space, the 'three colors' are only the spatial dimensions, rather than any property of physical substance. The existing 'three colors' can be merged into the wavefunction, described with the complex-quaternions.other existing theories are still unable to account for the color confinement, laying themselves open to suspicion. The assumption of color charge in the QCD is appealing for more validation experiments. Up to now, the QCD may not be really perfect yet, especially its fundamental assumption. c) Dark matter. The existence of the physical phenomena connected with the dark matters was firstly validated in the astronomy, and then was accepted generally by the whole academic circle. Nevertheless the Standard Model is blind to the existence of dark matters, and it is unable to elucidate the relevant physical phenomena either. Further the Standard Model and even the 'Beyond the Standard Model' are incapable of predicting or inferring the confirmed dark matters. It means that the research scope, in the mainstream of current unification theories, is restricted and insufficient enough. For the unification theory, which is unable to explore the dark matter, there may be still something left to be improved. Apparently an appropriate unification theory must be capable of comprising and exploring the ordinary matter and dark matter simultaneously.Presenting a striking contrast to the above is that it is able to account for a few problems, derived from the QCD and other existing theories, in the quantum mechanics described with the complex-sedenions, trying to improve the unificat...

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Gauge Invariance of Sedeonic Equations for Massive and Massless Fields

Cited by 9 publications

References 19 publications

Phenomenology from Dirac Equation with Euclidean-Minkowskian “Gravity Phase”

Phenomenology from Dirac Equation with Euclidean-Minkowskian “Gravity Phase”

Sedeonic equations of ideal fluid

Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

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