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I have been further working on the entry higher category theory and physics. There is still a huge gap between the current state of the entry and the situation that I am hoping to eventually reach, but at least now I have a version that I no longer feel ashamed of.
Here is what i did:
Partitioned the entry in two pieces: 1. “Survey”, and 2. “More details”.
The survey bit is supposed to give a quick idea of what the set of the scene of fundamental physics is. It starts with a kind of creation story of physics from $\infty$-topos theory, which – I think – serves to provide a solid route from just the general abstract concept of space and process to the existence and nature of all $\sigma$-model quantum field theories of “$\infty$-Chern-Simons theory”-type (which includes quite a few) and moreover – by invoking the “holographic principle of higher category theory” – all their boundary theories, which includes all classical phase space physics.
The Survey-bit continues with indicating the formalization of the result of quantizing all these to full extended quantum field theories. It ends with a section meant to indicate what is and what is not yet known about the quantization step itself. This is currently the largest gap in the mathematical (and necessarily higher categorical) formalization of physics: we have a fairly good idea of the mathematics that describes geometric background structure for physics and a fairly good idea of the axioms satisfied by the quantum theories obtained from these, but the step which takes the former to the latter is not yet well understood.
The “More details”-bit is stubby. I mainly added one fairly long subsection on the topic of “Gauge theory”, where I roughly follow the historical route that eventually led to the understanding that gauge fields are modeled by cocycles in higher (nonabelian) differential cohomology.
Apart from this I added more references and some cross-links.
I know that the entry is still very imperfect. If you feel like pointing out all the stuff that is still missing, consider adding at least some keywords directly into the entry.
added a section References – On topos-theoretic formulations of physics
Added sections
Phenomenological models: the standard model and gravity
(running out of steam towards the end)
References: … On functorial spectral geometry
have expanded the paragraph listing examples of (higher) gauge theories to a subsection gauge theory – classes of examples
The opening sentence is not good English
We discuss the set of the scene of fundamental physics.
Was the idea to use theatrical terms?
The opening sentence is not good English
Okay, thanks. I need to rephrase it then.
Was the idea to use theatrical terms?
Yes.
How about “the backdrop for fundamental physics”? Does that sound weird, too?
The backdrop can suggest it doesn’t structure the action very much. You do say figuratively about a place that it’s a ’stage’. E.g, about the Tower of London
It has been the stage on which much of England’s dramatic but often sad and bloody saga of royal history has been played out.
So
We discuss the stage on which fundamental physics is played out.
But perhaps setting is better.
We discuss the setting in which fundamental physics takes place.
Thanks, David! Very helpful. I have replaced in the entry the sentence with yourr suggestion.
I have started a section In phenomenology and experimental physics at higher category theory and physics. In reaction to this G+ discussion.
added pointer to
added pointer to this recent preprint:
Thanks for catching this. How about:
For a more coherent exposition, starting with introduction of the very basics, see also at geometry of physics.
But one day I’ll want to bring this entry here into better shape…
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