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seen Dec 18 at 22:16

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 here.


Feb
8
answered Are identity types interpreted physically in an infinity-topos formulation of equations of motion?
Feb
8
awarded  Announcer
Feb
7
answered Learning about super-symmetric quantum mechanics and integrable systems
Feb
5
awarded  Announcer
Feb
5
revised Hilbert, Gödel, and “God equations” - a 19th century lesson for 21st century physicists?
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Feb
5
revised Hilbert, Gödel, and “God equations” - a 19th century lesson for 21st century physicists?
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Feb
5
answered Hilbert, Gödel, and “God equations” - a 19th century lesson for 21st century physicists?
Feb
5
comment Did Hilbert publish general relativity field equation before Einstein?
...listed here: ncatlab.org/nlab/show/Einstein-Hilbert+action#History
Feb
5
comment Did Hilbert publish general relativity field equation before Einstein?
This is an excellent collection of quotes, thanks! It does seem to me, though, that Hilbert was quite fond of his way of deriving the equations and behind all the politeness was a feeling of superiority. Because in one of his "Lectures on the Foundations of Physics" that Hilbert gave a few days after Einstein's article surfaced he speaks of the work of Civita, Weyl, Schouten, Eddington and culminating in Einstein as a "colossal detour" and concludes that Einstein's equations confirm his variational computation is a "nice consistency check" (German: "schöne Gewähr"). See the citations listed..
Feb
4
comment Hilbert, Gödel, and “God equations” - a 19th century lesson for 21st century physicists?
Thanks Xiao-Gang Wen for this translation of the famous paragraph from the Dao-De-Jing. Re-reading it now it is striking how similar this is to Hegel's metaphysics in his "Science of Logic": ncatlab.org/nlab/show/Science+of+Logic
Feb
3
awarded  Announcer
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
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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").