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I am a postdoc in mathematics, but have my degree in theoretical physics. My work is about mathematical structures motivated from quantum field theory and string theory. For more see my personal web on the nLab.


Feb
3
comment String theory in the context of quantization prescriptions
I suppose what you are after may not be in the literature yet. But another among articles that study spaces of choices in producing string worldsheet QFTs (for the rational case, e.g. WZW) is Runkel et al.'s "Uniqueness of open/closed rational CFT with given algebra of open states" arxiv.org/abs/hep-th/0612306 .
Feb
2
comment String theory in the context of quantization prescriptions
One exception is Klaus Pohlmeyer and a few of his followers to this day. Pohlmeyer had been hoping that if one changes something about the string quantization prescription that then the critical dimension would go away, see the review here: arxiv.org/abs/hep-th/0403260 (together with an argument for why it does not). The latest work inspired by Pohlmeyer is arxiv.org/abs/1204.6263 , which gives a rigorous but perturbative quantization of the 2d Nambu-Goto action, claiming that the anomaly is not seen there.
Feb
2
comment String theory in the context of quantization prescriptions
I see what you are after here. Right, so I am not aware of a decent discussion of the space of geometric quantization choices on the string worldsheet itself, the usual Kähler polarization looks maybe too canonical to have inspired many to look for something else. One exception is..
Feb
2
revised String theory in the context of quantization prescriptions
deleted 12 characters in body
Feb
2
answered String theory in the context of quantization prescriptions
Jan
27
awarded  Nice Answer
Jan
23
comment Superspace as the Hilbert Space for Quantum Gravity
Take that as an exercise, to see that metrics don't form a vector space. But even if you considered field species that did form a linear space, it would in general not naturally be a Hilbert space, and crucially it wouldn't be the Hilbert space of quantum states of the theory.
Jan
22
comment Superspace as the Hilbert Space for Quantum Gravity
Yes, you can imagine building a Hilbert space of wavefunctions on Wheeler superspace. But it is not possible to "interpret superspace as a Hilbert space" (it's not even a vector space, to begin with), which is what you were asking.
Jan
22
comment Superspace as the Hilbert Space for Quantum Gravity
Wheeler superspace is the configuration space of "the cosmos" for a given cosmological model. The Hilbert space of states is instead formed by wave functions on that superspace. Gravitons are hard to see in this perspective, which is non-perturbative if done right (which is a big "if").
Jan
15
answered In which field theories with fermions do string- and fivebrane structures not come up?
Jan
12
awarded  Announcer
Jan
12
awarded  string-theory
Jan
12
revised about the Atiyah-Segal axioms on topological quantum field theory
edited body
Jan
11
answered about the Atiyah-Segal axioms on topological quantum field theory
Jan
11
comment about the Atiyah-Segal axioms on topological quantum field theory
Hey Trimok, what you write is just wrong and mixing things up. Please check first if you understand what a question is about before makeing statements like this.
Jan
11
comment How to treat differentials and infinitesimals?
On the other hand one can choose to build concrete models for the axioms in which notably the textbooks by Kock are written, hence for toposes that validate the Kock-Lawvere axioms. In the typical such models the category of smooth manifolds is enlarged somewhat by objects known as "smooth loci", which include for instance the space formally dual to the "ring of dual numbers", which is just the ring embodying the equation "epsilon^2 = 0". This more concrete incarnation of SDG can be phrased entirely in classical logic and hence shows which classical notions embody the idea of infinitesimals.
Jan
11
comment How to treat differentials and infinitesimals?
There are two complementary aspects to this. On the one hand the categorical logic of toposes allows to formally speak of the subset of the real line of elements that square to 0. This is just what people following Leibniz intuitively did anyway, but categorical logic shows that and how exactly this is consistent. This is then how notably Anders Kock (home.imf.au.dk/kock) wrote his two textbooks on synthetic differential geometry (home.imf.au.dk/kock/SGM-final.pdf): he speaks "synthetically" of the subset D of R on the elements that square to 0 and derives all of diff geometry.
Jan
9
comment What are the practical applications of quantum foundations?
Yes, I agree, one needs to be careful and I think the main message is that it is good to keep an open mind, either way. As in the last sentence of the quote above: "So it is a problem whether or not to worry about philosophies behind ideas"
Jan
9
awarded  Announcer
Jan
9
awarded  Nice Answer