All Questions
Tagged with big-list mp.mathematical-physics
18 questions
147
votes
43
answers
61k
views
Where does a math person go to learn quantum mechanics?
My undergraduate advisor said something very interesting to me the other day; it was something like "not knowing quantum mechanics is like never having heard a symphony." I've been meaning to learn ...
142
votes
17
answers
23k
views
What makes four dimensions special?
Do you know properties which distinguish four-dimensional spaces among the others?
What makes four-dimensional topological manifolds special?
What makes four-dimensional differentiable manifolds ...
97
votes
9
answers
7k
views
Examples where physical heuristics led to incorrect answers?
I have always been impressed by the number of results conjectured by physicist, based on mathematically non-rigorous reasoning, then (much) later proved correct by mathematicians. A recent example is ...
74
votes
16
answers
8k
views
Geometric / physical / probabilistic interpretations of Riemann zeta($n>1$)?
What are some physical, geometric, or probabilistic interpretations of the values of the Riemann zeta function at the positive integers greater than one?
I've found some examples:
1) In MO-Q111339 ...
67
votes
14
answers
23k
views
A reading list for topological quantum field theory?
Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic ...
39
votes
4
answers
5k
views
Interesting and surprising applications of the Ising Model
One of the most famous models in physics is the Ising model, invented by Wilhelm Lenz as a PhD problem to his student Ernst Ising. The one-dimensional version of it was solved in Ising's thesis in ...
- 3,515
36
votes
12
answers
18k
views
Open problems in PDEs, dynamical systems, mathematical physics
(This question might not be appropriate for this site. If so, I apologize in advance. I would have posted to mathstack, but I'm looking for advice from active researchers.)
I am an undergrad in math ...
36
votes
6
answers
11k
views
Open problems in mathematical physics
What are good, still unsolved problems in mathematical physics that are in vogue? I always get the same answers: reference to Millennium Problems by the Clay Institute, or "there's still a lot to do ...
32
votes
5
answers
3k
views
What is the status of the Hilbert 6th problem?
As you know, the Hilbert sixth problem was to axiomatize physics. According to the Wikipedia article, there is some partial succes in this field. For example, Classical mechanics, I believe, can be ...
- 7,426
18
votes
4
answers
4k
views
What are the "hot" topics in mathematical QFT at the time?
I am currently finishing my Master's studies in mathematical physics. One topic which always interested me a lot were modern mathematical approaches to Quantum Field Theory (QFT) as well as the ...
14
votes
5
answers
5k
views
Who says understanding physics helps mathematicians? (A reference request) [Take the word "who" literally.]
If I wanted to make a somewhat bold and rather vague claim in print that it is widely acknowledged among mathematicians that knowledge of mechanics (in the sense in which physicists understand that ...
14
votes
3
answers
1k
views
Can there be a polymath project for mathematical physics?
My hunch is that it might be possible to create something like https://polymathprojects.org/ for mathematical physics and I'd like to know whether MathOverflow users can recommend some appropriate ...
13
votes
2
answers
1k
views
Applications of non-separable Hilbert spaces
In applications, Hilbert spaces of interest are often assumed to be separable. In addition to being extremely convenient mathematically, this assumption can often be justified on computational or ...
9
votes
3
answers
1k
views
Bounding a spectral gap: what proof techniques exist?
The following situation is ubiquitous in mathematical physics. Let
$\Lambda_N$
be a finite-size lattice with linear size
$N$. An typical example would be the subset of
$\mathbb{Z}\times\mathbb{Z}...
6
votes
0
answers
211
views
What is known about "dimension two" vertex algebras?
In the paper Chiral Koszul duality, Gaitsgory and Francis develop a notion of a chiral algebra living on an arbitrary variety $X$. When $X=\mathbf{A}^1$ and the chiral algebra is translation invariant,...
3
votes
0
answers
270
views
Categorical General Relativity
What are some good references for GR from a categorical point of view?
This is essentially just a big-list reference request.
I'm aware that the subject exists and can do some basic sleuthing to find ...
1
vote
1
answer
235
views
Showing nonlinearity of PDEs arising from physics by mathematical argument alone
Roger Temam writes in SOME DEVELOPMENTS ON NAVIER-STOKES EQUATIONS IN THE SECOND HALF OF THE 20th CENTURY:
A remarkable property of the Navier-Stokes equations is that they are
one of the very ...
- 11
0
votes
1
answer
493
views
Physics that needs "new" math [closed]
Just curious: I can't think of a single example that a physicist did not had his mouth open in amazement when he learnt that all (OK, lets say the foundations) the math he needs for his brand-new ...
- 4,829