Re: Is that character *+A7AC LATIN CAPITAL LETTER SCRIPT G ?

From: Frédéric Grosshans <frederic.grosshans_at_gmail.com>
Date: Thu, 10 Jan 2013 15:46:55 +0100

Would you be able to provide a more complete copy of the article in question. It would allow those of us with the proper background to look for any other potential documents using the character in question.

A./

This book is still under copyright, since Louis de Broglie deceased in 1987, but I'm ready to send a scan of a few pages of the book to some of you, as soon as I scan them. However, I think that posting the extracts below to clarify the context of use of this character does not violate any law.

More information on the book and the excerpt where this character appears :

• Title : La théorie des particules de spin 1/2  (électrons de Dirac)
• Author : Louis de Broglie
• Edition : 1952, by Gauthier-Villars (Paris)
• Some URLS:
• http://books.google.fr/books/about/La_th%C3%A9orie_des_particules_de_spin_1_2.html?id=3qzvAAAAMAAJ&redir_esc=y
• http://www.worldcat.org/title/theorie-des-particules-de-spin-1-2-electrons-de-dirac/oclc/299670429/editions?referer=di&editionsView=true

The relevant character appears in pages 55 to 57. It corresponds to the following 'logical' subdivisions (in case you find another edition/translation):

• Chapitre IV : Les moments cinétiques propres du point de vue relativiste
• (Proper(?) angular momenta in a relativistic approach)
• 7. Théorie de M. Jan v. Weyssenhoff
• (Jan v. Weysenhoff theory)

The first   paragraphs (reproduced and translated below) of this part give the sources of the theory explained here, and states that this is just a summing up of this theory. This 'original' theory is maybe source of the notation,  and these paragraphs can help to define the "the proper background" you alluded to (which seems to be relativistic spin fluids).

M. Jan v. Weyssenhof a publié (1) une série de mémoires où developpant les idées de Mathisson, Lubanski et Frenkel il a établi une théorie relativiste des fluides à spin et des particules à spin. Une tentative a aussi été faite en France par M. Olivier Costa de Beauregard.

Je vais résumer ici brièvement, sans entrer dans tous les détails ni poursuivre les développements, quelques uns des calculs de M. v. Weyssenhoff pour montrer leur liaison avec les concepts exprimés ci-dessus.

(1) Acta Physica Polonica, vol. IX, pp. 8-53

My quick and dirty translation :

Mr Jan v. Weysenhoff published (1) a series of papers where he developed the ideas of Mathisson, Lubanski and Frenkel into a relativistic theory of spin-fluids and spin-particles. An attempt also has been made by Mr Olivier Costa de Beauregard.

I will here briefly sum up, without giving all the details nor following all developments, some of Mr. v. Weyssenhoff's calculations to show their link with the concepts expressed previously.

(1) Acta Physica Polonica, vol. IX, pp. 8-53

When he introduces  the notation, on the next page, he says (where ĝ stands for the "new" character):

[...] M. Weyssenhoff, adoptant un point de vue dont M. Costa de Beauregard a plusieurs fois souligné l'importance, ne suppose pas le tenseur Tᵅᵝ symétrique et écrit :

Tᵅᵝ=ĝᵅuᵝ

où ĝᵅ est le quadrivecteur "densité propre d'impulsion linéaire" [...]

[...]Mr Costa de Beaureagard has underlined several times the importance of the point of view adopted by Mr Weyssenhoff, where he does not suppose the tensor Tᵅᵝ to be symmetrical and writes:

Tᵅᵝ=ĝᵅuᵝ

where ĝᵅ is the four-vector "linear momentum proper(?) density"[...]

I wasn't able to find the cited paper on the web, but I plan to ask my librarian. It dates from 1947, and seems to be cited often in works about the history of relativity.

   Frédéric


Received on Thu Jan 10 2013 - 08:47:17 CST