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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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
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 …
Hollis Williams's user avatar
29 votes
2 answers
4k views

Formal mathematical definition of renormalization group flow

I was watching some lectures by Huisken where he mentioned that one-loop renormalization group flow was in some analogous to mean curvature flow. I have tried reading up the exact definition of what …
Hollis Williams's user avatar

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