# Dirac Equation in GA (Proca)

The are several references to a set of papers by Proca about 1930 presenting the (1928) Dirac Equation using Clifford Algebra. Would anyone know how to access these papers?

I did not know this existed. Great paper, very well written, and even containing some ideas that have not been followed up on (mass as fifth dimension, dual to de Broglie wavelength).

Browsing the website of this translator, there is wonderful material everywhere, all the classics in one place. What a great resource, what a great service to the community. Let’s all thank him!

Prof Dorst: Thank you for this. I probably could have handled the French original, but a translation as well!

To these classics I would suggest adding

Essai sur la géométrie à $n$ dimensions

which is Camille Jordan’s article on n-dimensional geometry, which is hyperplane-based. G W Stewart has commented and translated the first half. It is interesting to read how Jordan stick-handles about the k-outer product of hyperplanes since he considers it as defined by the set of points whose coordinates satisfy k independent linear equations. About the same time, Jordan co-invented the SVD, and of course the Jordan canonical form; apparently useful in theory, poor for calculations.

Sorry for capturing the topic: From the link there I found some links to papers about “premetric” electrodynamics. There, the different authors formulate Maxwell’s equations with the help of differential forms and start at the charge conservation (where the charge-current is modelled as a 3-form). Based on this, they formulate the equations with sources and the source-free equations with help of the exterior derivative and therefore metric-free. They argue that the only point, where the metric could enter the Maxwell equations is the constitutive equation where the field strengths and the excitations are coupled. Is there any possibility to show this metric-free formulation of Maxwell equations with the help of GA (maybe STA)? I have difficulties to understand how this could be achieved, since Maxwell’s equations are in the form \nabla \cdot G = J and \nabla \wedge F = 0. The charge conservation can be calculated by \nabla \cdot J = 0 if I recall correctly. But, is it possible to go from the charge conservation to the G equation and use the G as some type of potential? And further, is \nabla \cdot metric free, since it is an inner product?

I rely of GA4P for Maxwell’s equation(s), and cannot reply to your question. But I notice that after Proca’s work on the Dirac equation using GA, Juvet had the little paper Opérateurs de Dirac et équations de Maxwell par G Juvet, Lausanne, 1930, in which he used the same GA basis elements (called ‘des nombres hypercomplexe’ for Maxwell’s equations as Proca used for the Dirac equation…

What is GA4P? Sorry for a maybe silly question

Geometric Algebra for Physicists.

Thanks for clarification!