All Questions
7 questions
122
votes
7
answers
15k
views
Topology and the 2016 Nobel Prize in Physics
I was very happy to learn that the work which led to the award of the 2016 Nobel Prize in Physics (shared between David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz) uses Topology. In ...
2
votes
1
answer
149
views
Surveys/monographs on the vortex filament equation
Where can I find surveys on the mathematical aspects of the vortex filament equation?
In particular, I'm interested in the following topics:
physical motivation;
notion of solutions and ...
- 277
0
votes
1
answer
124
views
Relationship between the vortex filament equation and the cubic Schrödinger equation
How is the vortex filament equation
$$\partial_t \chi = \partial_s \chi \wedge \partial_{ss} \chi,$$
where $\chi(t,s)$ is a curve in $\mathbb R^3$,
related to the cubic Schrödinger equation?
Note 1. ...
- 277
14
votes
5
answers
4k
views
References for classical Yang-Mills theory
I am looking for a reference to study classical (i.e., not quantized) Yang-Mills theory.
Most of the sources I find focus on mathematical aspects of the theory, like Bleecker's book Gauge theory and ...
- 1,064
1
vote
0
answers
75
views
Derivation of the vortex filament equation from Euler equation
How can the vortex filament equation
$$\partial_t \chi = \partial_s \chi \wedge \partial_{ss} \chi,$$
where $\chi(t,s)$ is a curve in $\mathbb R^3$,
be derived from the Euler equation
$$\partial_t \...
- 277
4
votes
1
answer
710
views
Reference request for instantons
I've been researching instantons lately and I'd like to learn more about them but would like some help finding what to read. I have read about the ADHM equations and their noncommutative analogues. ...
- 161
0
votes
0
answers
64
views
Relationship between the vortex filament equation and the transport equation
Let us consider the vortex filament equation
$$\partial_t \chi = \partial_s \chi \wedge \partial_{ss} \chi,$$
where $\chi(t,s)$ is a curve in $\mathbb R^3$.
How is the Cauchy problem for the ...
- 277