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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
2
votes
0
answers
65
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Link between Extended Supergauge Group and Twistor Theory
In a 1974 paper on supergauge transformations in four dimensions, Wess and Zumino considered an extended supergauge group which contains the conformal group as a subgroup. An interesting thing about …
11
votes
1
answer
604
views
Are there currently any plausible approaches to proving the Penrose сonjecture?
I have recently been reading some of the literature on the Penrose inequality, especially the papers by Bray and by Huisken and Ilmanen.
One notices immediately that the existing proofs for the Penro …
5
votes
0
answers
357
views
Research Problem combining Algebraic Geometry and QFT
A student who specialises in algebraic geometry has contacted me to ask if they could collaborate with me on some problem which relates mathematical physics and algebraic geometry. I think his idea i …
15
votes
2
answers
1k
views
Counterexamples to the Penrose Conjecture
I have noticed that in the literature on causality in general relativity one sees apparent counterexamples to the cosmic censorship hypothesis (somehow you have models for gravitational collapse which …
3
votes
0
answers
175
views
Lifting in String Theory and QFT
I'm posting this here instead of Physics Stack as my question is on the precise mathematical meaning of a word which is often used in the physics literature.
In theoretical physics (especially string …
0
votes
1
answer
129
views
Generalising results on superfluid Kubo formulas
In a 2014 article by Chapman, Hoyos and Oz, the authors study non-equilibrium fluid dynamics and describe a method for deriving Kubo formulas for thermal transport coefficients of superfluids (the met …
9
votes
1
answer
695
views
Non-commutative complex geometry
I was reading a physics paper where it was mentioned that the basic framework of Connes' differential non-commutative geometry (or actually, a slight modification of Connes in that paper) would need s …
9
votes
0
answers
310
views
Proving the Hawking Area Theorem without Cosmic Censorship
I notice that some of the classic results and theorems in black hole physics from the 1960s like the Hawking area theorem use the cosmic censorship hypothesis at some point in the proofs of the theore …
5
votes
0
answers
153
views
Associating noncommutative geometries to 2D conformal field theories
I have recently been reading a bit about noncommutative geometry and string theory and it looked to be an open question (or at least this was open two decades ago) whether there are constructions whic …
3
votes
1
answer
198
views
Supersymmetric SYK Model in 3D?
In a 2017 article More on supersymmetric and 2d analogs of the SYK model by Murugan, Stanford and Witten, the authors take a model called the SYK model (named after Sachdev, Ye and Kitaev) and study s …
22
votes
2
answers
3k
views
Is Witten's proof of the positive mass theorem rigorous?
I noticed that the only official reason given for awarding Edward Witten the Fields medal was his 1981 proof of the positive mass theorem with spinors, so I was assuming that the proof was fully rigor …
9
votes
1
answer
274
views
Physics application of Wilson surface observables
There is some work which generalises the usual Wilson loop in QFT to higher dimensions and constructs non-abelian Wilson surface functionals in the context of non-abelian gerbes.
It seems to me that t …
10
votes
0
answers
263
views
Physical Approach to Knot Categorification
Some recent work by Aganagic on knot categorification, Knot Categorification from Mirror Symmetry, Part II: Lagrangians, discusses two categorical approaches to categorification of quantum link invari …
12
votes
1
answer
566
views
Alternative approaches to topological QFTs
A while ago I read the paper 'Quantum Field Theory and the Jones Polynomial' by Edward Witten. This article uses a lot of concepts from physics like BRST symmetry and the Chern-Simons action which ar …
2
votes
0
answers
40
views
Intuition behind oscillating eigenvalues for inhomogeneous Sturm-Liouville problem
I was looking at an article where the author finds an example of a solotone effect in a heat transfer context of a 1D layered composite rod rather than the usual metal rod made out of one material (s …