[General] 21st century linear, first order theories. Are there any others?

[John Williamson]

Dear all,

I’m just writing a paper on the new linear set of differential equations I proposed last year and want to compare it to similar work in the 21st century, or fairly recently at least. I usually like to read a couple of papers before breakfast (thanks for keeping me supplied guys – especially David John D and Al) – but I’m just drawing a blank here. What should I be looking at?
To be specific:  is anyone aware of any other equations which have been proposed this century or in the second half of last century which can be written in the linear first-order form d (something) = 0?

For reference, what comes to mind in the early twentieth are the Dirac equation and the Weyl equation. There were other guys playing with things around then, but my mind has gone blank (Eddington?). Shroedinger’s, of course, has second order derivatives (though, as Dieks has argued it has first order features imported though the adoption of the de Broglie relation – and I am going to refer to that). I’m also not talking about further work on Dirac or Maxwell such as that by Hestenes or using the Bateman method on the Maxwell equations (of which the most advanced work, in my view, is that of Martin which he and I will review over the Christmas “vacation”). I’m talking about proper, basic, first order equations of light, matter or anything else.

David – you were proposing I write a review of comparable work (and I am delighted that you are going to review the various electron models!) – but I’m talking here about linear theories expressed in (vector) differential form, not about any specific model within them. Tony … your stuff is brilliant but second order – anything else you are aware of?  Nick … Pask’s stuff was brilliant too – did he express anything new in linear equations? Also, of course, not referring to work on such perturbative theories as QED and non-perturbative stuff such as QCD, most of the “standard model” and the various string theories. Chip, Albrecht, Richard ... you have been looking at lots of electron and photon models - anything there? Joakim, Adam, Mayank ... anything caught your attention? Chandra, Al, Martin … anything on light beyond Maxwell or in “quantum entanglement”? Michael M, David, Viv … anything out there in space?

Maybe I’m being stupid at this time in the morning and more things will come to me after another cup of coffee, but I’m drawing a blank here.  Any further suggestions would be helpful!

Regards, John.
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