Is Prequantum Field Theory Worth Exploring?

In summary, this conversation is about a mathematical physicist who writes about complex analysis and dark matter.
  • #1
Urs Schreiber
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Urs Schreiber submitted a new PF Insights post

Examples of Prequantum Field Theories IV: Wess-Zumino-Witten-type Theories

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  • #2
"The bouquet which emanates form these..." should be FROM. Also various pieces of latex didn't compile.

Have you seen any other interesting bouquets? What would happen in the complex analytic world? I see there is some gauge theoretic interest in complex analytic superspaces, $$mathbb{C]^{p|q)$$, such as p. 12 of http://arxiv.org/abs/1507.03048.
 
  • #3
David Corfield said:
"The bouquet which emanates form these..." should be FROM. Also various pieces of latex didn't compile

Thanks for catching this! All fixed now.

David Corfield said:
Have you seen any other interesting bouquets?

We had looked a bit into the higher tower of cocycles emanating from a semisimple Lie algebra, which in the first stage yields 3d-Chern-Simons theory on G-gauge fields, in the second stage yields 7d-Chern-Simons theory on String(G)-higher gauge fields, and then in the next stage yields an 11-dimensional CS theory that Hisham argues is related to the "M9-brane".

David Corfield said:
I see there is some gauge theoretic interest in complex analytic superspaces, such as p. 12 of http://arxiv.org/abs/1507.03048.

Yes, superstring perturbation theory in principle is all about complex analytic supergeometry, due to it being all about super Riemann surfaces.
 
  • #4
what's the point of this mystical, arcane stuff? It seems like you've used extremely dense, convoluted language to construct a model that doesn't appear to describe nature.

I'm just a humble biologist here.
 
  • #5
glaucousNoise said:
what's the point of this mystical, arcane stuff? It seems like you've used extremely dense, convoluted language to construct a model that doesn't appear to describe nature.

He is a mathematical physicist. Its the type of thing they do - eg delve deeply into the underlying mathematical structure of our theories.

My background is math, and the detail of what he writes is way beyond my present level. But you can still read it and glean bits and pieces here and there that are interesting.

Thanks
Bill
 

What is a prequantum field theory?

A prequantum field theory is a theoretical framework that attempts to unify quantum mechanics and general relativity by describing the fundamental particles and forces of the universe as fields on a prequantum spacetime manifold.

What is the significance of the Wess-Zumino-Witten-type theories in prequantum field theory?

The Wess-Zumino-Witten-type theories are important examples of prequantum field theories that have been extensively studied and have provided insights into the mathematical structure of these theories.

How do Wess-Zumino-Witten-type theories differ from other prequantum field theories?

Wess-Zumino-Witten-type theories are characterized by their use of non-Abelian gauge symmetries and their inclusion of topological terms in the action, which can lead to non-trivial effects such as the emergence of fractional spin particles.

What are some of the open questions and challenges in Wess-Zumino-Witten-type theories?

Some of the unresolved issues in Wess-Zumino-Witten-type theories include the problem of ultraviolet divergences, the lack of a complete mathematical framework for these theories, and the difficulty in obtaining physically meaningful predictions from them.

How do Wess-Zumino-Witten-type theories relate to other areas of theoretical physics?

Wess-Zumino-Witten-type theories have connections to various other areas of theoretical physics such as conformal field theory, string theory, and topological quantum field theory. They also have applications in condensed matter physics and cosmology.

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