The Lorentz invariance of the wave equation for the electric potentialφemerged before the formulation of Einstein's special relativity. The builtin covariance of Maxwell's equations comes to light more clearly when using four-vector or even tensor notation....
72, each TTN variational sweep could be parallelized in a way to optimize its tensors separately on different computing nodes, so as to optimally scale the computational resources with the system size. On top of this, the implementation of tensor contractions on GPUs could be used to speed up...
However, since the field-strength tensor F is not closed, we cannot introduce a gauge potential A such that F = dA in the standard way, making quantization difficult. Instead of using the Zwanziger formalism as in [15], we aim to rewrite these equations in standard form via a field ...
2 Nonlinear electrodynamics For the sake of completeness and to emphasize how the NLE equations arise, pointing out their structure and the need of introducing a new skew symmetric tensor, Pμν, in addition to the electromagnetic field tensor fμν, we present in this section the derivation ...
Photon Mass Effects 600 12.9 Effective Photon Mass in Superconductivity; London Penetration Depth 603 12.10 Canonical and Symmetric Stress Tensors; Conservation Laws 605 12.11 Solution of the Wave Equation in Covariant Form; Invariant Green Functions 612 References and Suggested Reading 615 Problems 617 ...
E. Hay's Vector and Tensor Analysis, Chapter 1, Section 7 (dot product) and Section 8 (cross product). Problem 1.2 The triple cross-product is not in general associative. For example, suppose A = ~ and C is perpendicular to A, as in the diagram....
7.10 Scattering of a Relativistic Particle with a Spin in the Coulomb Field 653 7.11 Green's Functions of Electron-Positron and Electromagnetic Fields 657 7.12 Interaction between Electrons and Muons 662 7.13 Higher-Order Corrections 667 7.14 Answers and Solutions 669 ...
ofFμνandFμνElectrodynamics in Rotating Reference FramesMaxwell Equations in Exterior Differential FormsProposal of New NotationdΛ for Exterior Derivative#Electrodynamics in Tensor Formulation#Electrodynamics under Galilean Transformation#EM Field in the Form of Contravariant TensorFμν#EM Field in the ...
The difficulties associated with infinite self-energies and mass renormalization are absent from this theory and a consistent set of energy-momentum and angular-momentum conservation laws follows from the associated energy-momentum tensor. The mechanism of "measurement" radiation is discussed and is ...
E. A. Kuraev, N. P. Merenkov, and V. S. Fadin, “The Compton effect tensor with heavy photon,” Sov. J. Nucl. Phys.45, 486 (1987). Google Scholar D.Bardin, S.Bondarenko, L.Kalinovskaya, et al., “SANCnews: Sector f f b b, " Comput. Phys. Commun.177, 738–756 (2007...