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touched the formatting at additive category
brief category:people-entry for hyperlinking references at super Poincaré Lie algebra and supersymmetry
brief category:people-entry for hypoerlinking references at super Poincaré Lie algebra and supersymmetry
I’ll be working a bit on supersymmetry.
Zoran, you had once left two query boxes there with complaints. The second one is after this bit of the original entry (this will change any minute now)
The theory of supergravity is, as a classical field theory, an action functional on functions on a supermanifold which is invariant under the super-diffeomorphism group of .
where you say
Zoran: action functional is on paths, even paths in infinitedimensional space, but not on point-functions.
I think you got something mixed up here. If is spacetime, a field on is the “path” that you want to see. The statement as given is correct, but I’ll try to expand on it.
The second complaint is after where the original entry said
many models that suggest that the familiar symmetry of various action functionals should be enhanced to a supersymmetry in order to more properly describe fundamental physics.
You wrote:
This is doubtful and speculative. There are many models which have supersymmetry which is useful in their theoretical analysis, but the same models can be treated in formalisms not knowing about supersymmetry. Wheather the fundamental physics needs a model which has nontrivial supersymmetry is a speculative statement, and I disagree with equating theoretical physics with one direction in “fundamental physics”. I do not understand how can a model suggest supersymmetry; it is rather experimental evidence or problems with nonsupersymmetric models. Also one should distinguish the supersymmetry at the level of Lagrangean and the supersymmetry which holds only for each solution of the equation of motion.
I’ll rephrase the original statement to something less optimistic, but i do think that supersymmetry is suggsted more by looking at the formal nature of models than by lookin at the nature of nature. If you have a gauge theory for some Lie algebra (gravity, Poincaré Lie algebra) and the super extension of the Lie algebra has an interesting classification theory (the super Poincar´ algebra) then it is more th formalist in us who tends to feel compelled to investigate this than the phenomenologist. Supersymmetry is studied so much because it looks compelling on paper. Not because we have compelling phenomenological evidence. On the contrary.
So, if you don’t mind, I will remove both your query boxes and slightly polish the entry. Let’s have any further discussion here.
brief category:reference-entry for hyperlinking
Mikhail Shifman (ed.)
The Many Faces of the Superworld
Yuri Golfand memorial volume
World Scientific, 2000
I started a bare minimum at quantum probability (redirecting noncommutative probability space etc.)
Some entries have long been secretly referencing such an entry, and I have cross-linked accordingly, for instance from von Neumann algebra and quantum computing.
I had the feeling somewhere we already had a detailed account of probability theory dually in terms of von NNeumann algebras, but if we do I didn’t find it(?)
I have been adding some material to matroid. I haven’t gotten around to defining oriented matroid yet (and of course there’s much besides to add).
expanded the section Idea – In brief at Bohr topos just a little bit, in order to amplify the relation to Jordan algebras better (which previously was a bit hidden in entry).
Since no one objected to my offer, I started a stub for the Kochen-Specker theorem and will continue working on it a bit later.
added to exceptional generalized geometry two examples of reductions of stucture groups that encode higher supersymmetry in 11d sugra.
have added a minimum on the level decompositon of the first fundamental rep of here.
added a bunch of references to M2-brane
for completeness, I have splitt off superstring from string
added this, under References – Review:
In March 2013, following an accurate processing of available measurement data, the Planck Scientific Collaboration published the highest-resolution photograph ever of the early Universe when it was only a few hundred thousand years old. The photograph showed galactic seeds in sufficient detail to test some nontrivial theoretical predictions made more than thirty years ago. Most amazing was that all predictions were confirmed to be remarkably accurate. With no exaggeration, we may consider it established experimentally that quantum physics, which is normally assumed to be relevant on the atomic and subatomic scale, also works on the scale of the entire Universe, determining its structure with all its galaxies, stars, and planets.
started self-dual higher gauge theory. Just minimal idea and list of references so far.
added a bunch of further links, and made Dmitry Volkov a redirect
I have incorporated Jonas’ comment into the text at pretopos, changing the definition to “a category that is both exact and extensive”, as this is sufficient to imply that it is both regular and coherent.