Talk:Riemann–Silberstein vector

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Completeness

Reading this article for the first time, certain comments come to mind, which could guide edits:

The underlying abstract algebraic structure being used is unclear and should be stated. In particular, is it spacetime algebra with i being the unit pseudoscalar (as would be suggested by the use of the term multivector), its complexification (the Dirac algebra) with i being the imaginary unit, or is it simply a complexification of 3-D vectors in Gibbs's classic vector algebra? The third source (Bialynicki-Birula) implicitly treats it as the last of these, which is not directly compatible with the term multivector. The second equation adds scalars and vectors, suggestion the algebra of physical space. If this is the case, to avoid sloppiness, care must be taken to identify the symbol i in Cℓ_3,0(R), though this could be left to the article APS if that is stated as the formalism being used, though I'd suggest use of the term biparavector in place of multivector. Done
An orphan symbol S is used in a formula. This should be named. I suspect that it is the Poynting vector, and it would be worthwhile giving its formula here if the symbol is used. Done
It is difficult to relate the fundamental invariants and the energy density and momentum density to the expressions then given. It would make sense to give these symbols and to equate expressions of these to the existing expressions.

Thus it seems probable to me that the Riemann–Silberstein "vector" is the quantity (a biparavector) used in the algebra of physical space to describe the electromagnetic field. Perhaps this could be used as a model for the first sentence. — Quondum 08:26, 3 September 2012 (UTC)[reply]

If it's ok I added many more links, reformatted the article with section headings, and added the {{electromagnetism}} template. Maschen (talk) 08:12, 4 September 2012 (UTC)[reply]

Problematic symbol i

The use if the symbol i as the unit pseudoscalar presents problems in association with the Pauli matrices, because in that context is used as the imaginary unit. As such, it is used simultaneously to represent two distinct concepts, and introduces potential for confusion, even though in this context it seems to make no difference which is used in the formula (much like scalar multiplication by 1 is the same as matrix multiplication by the identity matrix). — Quondum 09:10, 4 September 2012 (UTC)[reply]

It was used in maths of em field, if i is not defined here how will people know? By all means change it to the correct definition if the current form is problematic. For now it has been removed. Maschen (talk) 09:17, 4 September 2012 (UTC)[reply]

Done. — Quondum 10:52, 4 September 2012 (UTC)[reply]

physical units problem?

E has the unit N/As while cB has the unit N/Vs so they should mot be added, but I may have screwed up my calculation. Please add a line or two showing how the units fit together. — Preceding unsigned comment added by 80.133.150.253 (talk) 13:44, 22 January 2017 (UTC)[reply]

Hacyan & Maksoud

The following was moved from Ludwik Silberstein:

The Armenian scientist Shahin Hacyan developed the Riemann-Silberstein matrix in his 2018 scientific paper titled "The Riemann-Silberstein vector in the Dirac algebra". The Syrian researcher Hosam Mahmoud Maksoud put the Riemann-Silberstein matrix in Proca’s equation and used the coordinates to obtain all the particles (fermions and bosons) with one equation called the SHAAM Equation to reveal the source of mass and the shape of the electron. He studies the electron electromagnetically for the first time in his scientific paper. 2023: "The Electromagnetic Operator of Mass".

Rgdboer (talk) 23:45, 27 April 2024 (UTC)[reply]