Observers and splitting structures in relativistic electrodynamics

@article{Auchmann2014ObserversAS,
  title={Observers and splitting structures in relativistic electrodynamics},
  author={Bernhard Auchmann and Stefan Kurz},
  journal={Journal of Physics A},
  year={2014},
  volume={47},
  pages={435202}
}
We introduce a relativistic splitting structure as a means to map fields and equations of electromagnetism from curved four-dimensional space?time to three-dimensional observer?s space. We focus on a minimal set of mathematical structures that are directly motivated by the language of the physical theory. Space?time, world-lines, time translation, space platforms and time synchronization all find their mathematical counterparts. The splitting structure is defined without recourse to coordinates… 
View PDF on arXiv
10 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
1

10 Citations

Citation Type

Citation Type

Electrodynamics in noninertial frames
Abstract The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame…
Electrodynamics in noninertial frames
  • Y. Obukhov
  • Physics, Mathematics
    The European Physical Journal C
  • 2021
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The…
Discretization of Maxwell’s Equations for Non-inertial Observers Using Space-Time Algebra
We employ classical Maxwell’s equations formulated in space-time algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any…
Evolutionary equations and constraints: Maxwell equations
By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the…
Encoding electromagnetic transformation laws for dimensional reduction
TLDR
Within this contribution, the partial derivative and the corresponding chain rule for multivariate calculus are investigated with respect to their encodability in computational terms and target the layer above univariate calculus, but below tensor calculus.
Generally covariant Maxwell theory for media with a local response: Progress since 2000
In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful…
On the metamorphoses of Maxwell's equations during the last 150 years — spotlights on the history of classical electrodynamics
We outline Maxwell's five decisive papers on his equations governing electrodynamics (1862-1868). We study the metamorphoses of these equations and find essentially twelve different versions of them.…
Covariant variational evolution and Jacobi brackets: Particles
The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of…
PROTON-BEAM MACRO-PARTICLE INTERACTION: BEAM DUMPS AND QUENCHES
We derive a model for the time evolution of beam losses due to macro particles falling into the LHC proton beam. The macro-particle initial longitudinal and transverse location, as well as its size…
Covariant Variational Evolution and Jacobi brackets: Fields
The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of func...

References

SHOWING 1-10 OF 67 REFERENCES
The Large Scale Structure of Space-Time
TLDR
The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.
Space Geometry of Rotating Platforms: An Operational Approach
We study the space geometry of a rotating disk both from a theoretical and operational approach; in particular we give a precise definition of the space of the disk, which is not clearly defined in…
Kinematical conditions in the construction of spacetime
We adopt the point of view that a solution of Einstein's equations is an evolution of given initial Cauchy data. Implementing the evolution equations necessarily requires a determination, not…
Space Geometry in Rotating Reference Frames: A Historical Appraisal
The problem of giving a relativistic description of the geometry of a rotating disk has a history nearly as old as that of the theory of relativity itself. Already in 1909 Ehrenfest formulated his…
Simultaneity and generalized connections in general relativity
Stationary extended frames in general relativity are considered. The requirement of stationarity allows one to treat the spacetime as a principal fibre bundle over the one-dimensional group of time…
Dimensional reduction of field problems in a differential‐forms framework
Purpose – The purpose of this paper is to present a geometric approach to the problem of dimensional reduction. To derive (3 + 1) D formulations of 4D field problems in the relativistic theory of…
The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram
1 Introduction.- Part I Analysis of variables and equations.- 2 Terminology revisited.- 3 Space and time elements and their orientation.- 4 Cell complexes.- 5 Analysis of physical variables.- 6…
Nonlinear connections and 1+3 splittings of spacetime
The analogy between 1+3 splittings of the spacetime tangent bundle and the splitting of the tangent bundle to the bundle of linear frames into vertical and horizontal sub-bundles is described from…
Is the Lorentz signature of the metric of spacetime electromagnetic in origin
Theory of Electrodynamics in Media in Noninertial Frames and Applications
The theory of local electrodynamics of media in given noninertial frames, within the Maxwell‐Einstein theory, is constructed in terms of local observable EM fields and physical media parameters of…
...
1
2
3
4
5
...