scholarly journals Electromagnetic Field Equation and Lorentz Gauge in Rindler Space-time

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Electromagnetic Field ◽  
Gauge Transformation ◽  
Maxwell Equations ◽  
Space Time ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Lorentz Gauge ◽  
Rindler Space ◽  
Differential Operation ◽  
Gauge Fixing

In this paper, we derived electromagnetic field transformations and electromagnetic field equations of Maxwell in Rindler space-time in the context of general theory of relativity. We then treat the Lorentz gauge transformation and the Lorentz gauge fixing condition in Rindler space-time and obtained the transformation of differential operation, the electromagnetic 4-vector potential and the field. In addition, charge density and the electric current density in Rindler spacetimeare derived. To view the invariance of the gauge transformation, gauge theory is applied to Maxwell equations in Rindler space-time. In Appendix A, we show that the electromagnetic wave function cannot exist in Rindler space-time. An important point we assert in this article is the uniqueness of the accelerated frame. It is because, in the accelerated frame, one can treat electromagnetic field equations.

scholarly journals Quantization of Electromagnetic Field and Potential in Rindler Space-Time

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Electromagnetic Field ◽  
Inertial Frame ◽  
Space Time ◽  
Gauge Condition ◽  
Electromagnetic Potential ◽  
Lorentz Gauge ◽  
Rindler Space

The article treats quantization of electromagnetic field that is defined in Rindler space-time. Likely the electromagnetic field, the potential did quantizated in inertial frame, the electromagnetic field, the potential can quantizate by the transformation of electromagnetic field or the transformation of the potential in the accelerated frame. We treat Lorentz gauge condition in quantization of electromagnetic potential.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

A new approach on electromagnetism with dual number coefficient octonion algebra

2016 ◽  
Vol 13 (09) ◽  
pp. 1630013 ◽  
Author(s):  
Bhupesh Chandra Chanyal ◽  
Sunil Kumar Chanyal ◽  
Özcan Bektaş ◽  
Salim Yüce
Keyword(s):  
Maxwell Equations ◽  
Wave Equations ◽  
Space Time ◽  
Internal Space ◽  
Field Equations ◽  
Octonion Algebra ◽  
New Approach ◽  
Dual Number ◽  
Symmetrical Form ◽  
Unit Formula

Dual number coefficient octonion (DNCO) is one of the kind of octonion, it has 16 components with an additional dual unit [Formula: see text]. Starting with DNCO algebra, we develop the generalized electromagnetic field equations of dyons regarding the DNCOS spaces, which has two octonionic space-times namely the octonionic internal space-time and the octonionic external space-time. Besides, the generalized four-potential components of dyons have been expressed with respect to the dual octonion form. Furthermore, we obtain the symmetrical form of Dirac–Maxwell equations, and the generalized potential wave equations for dyons in terms of the dual octonion. Finally, we conclude that dual octonion formulation is compact and simpler like octonion formulation.

The General Theory of Relativity and Gravitation

2019 ◽  
pp. 426-460
Author(s):  
David D. Nolte
Keyword(s):  
Metric Space ◽  
Ricci Tensor ◽  
Mass Density ◽  
Geodesic Equation ◽  
Space Time ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Schwarzschild Metric ◽  
Curved Space ◽  
Invariant Element

The intrinsic curvature of a metric space is captured by the Riemann curvature tensor, which can be contracted to the Ricci tensor and the Ricci scalar. Einstein took these curvature quantities and constructed the Einstein field equations that relate the curvature of space-time to energy and mass density. For an isotropic density, a solution to the field equations is the Schwarzschild metric, which contains mass terms that modify both the temporal and the spatial components of the invariant element. Consequences of the Schwarzschild metric include gravitational time dilation, length contraction, and redshifts. Trajectories in curved space-time are expressed as geodesics through the Schwarzschild metric space. Solutions to the geodesic equation lead to the precession of the perihelion of Mercury and to the deflection of light by the Sun.

Generalization of London equations with space-time sedeons

2020 ◽  
pp. 2150039
Author(s):  
Victor L. Mironov
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Space Time ◽  
Normal Phase ◽  
Superconducting Phase ◽  
Combined System ◽  
Vector Potentials ◽  
Phenomenological Equations ◽  
External Sources ◽  
London Equations

We discuss the generalization of phenomenological equations for electromagnetic field in superconductor based on algebra of space-time sedeons. It is shown that the combined system of London and Maxwell equations can be reformulated as a single sedeonic wave equation for the field with nonzero mass of quantum, in which additional conditions are imposed on the scalar and vector potentials, relating them to the deviation of charge density and currents in the superconducting phase. Also, we considered inhomogeneous equations including external sources in the form of charges and currents of the normal phase. In particular, a screening of the Coulomb interaction of external charges in a superconducting media is discussed.

On a duality invariant action principle in vacuum electrodynamics

1970 ◽  
Vol 48 (20) ◽  
pp. 2423-2426 ◽  
Author(s):  
G. M. Levman
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Lagrangian Density ◽  
Vacuum Field ◽  
Field Tensor ◽  
Field Equations ◽  
Invariant Action ◽  
Electromagnetic Field Tensor ◽  
Derivatives Of

Although Maxwell's vacuum field equations are invariant under the so-called duality rotation, the usual Lagrangian density for the electromagnetic field, which is bilinear in the first derivatives of the electromagnetic potentials, does not exhibit that invariance. It is shown that if one takes the components of the electromagnetic field tensor as field variables then the most general Lorentz invariant Lagrangian density bilinear in the electromagnetic fields and their first derivatives is determined uniquely by the requirement of duality invariance. The ensuing field equations are identical with the iterated Maxwell equations.

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