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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
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 …
3 votes
1 answer
348 views

Coulomb branch varieties and symplectic singularities

I was recently looking at the survey article of Fu on symplectic resolutions which has a number of open questions and conjectures at the end. (I think one of these was existence of a classification o …
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 …
2 votes
0 answers
65 views

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 …
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 …
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 …
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 …
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 …
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 …
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 …
2 votes

What is the best place to learn about the mathematical foundations of quantum mechanics?

Another possibility might be Mackey's Mathematical Foundations of Quantum Mechanics (Mackey obviously being an eminent researcher in functional analysis and noncommutative geometry). A positive review …
Hollis Williams's user avatar
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
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 …
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 …
4 votes
Accepted

Counterexamples to the Penrose Conjecture

Having thought about this more and discussed it with others, the answer seems to be that there are likely no counterexamples to the Penrose inequality, even if one allows for unphysical violations. Fo …
Hollis Williams's user avatar

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