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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

33 votes
6 answers
5k views

What's "geometric algebra"?

Sometimes one bumps into the name "geometric algebra" (henceforth "GA"), in the sense of this Wikipedia article. Other names appear in that context such as "vector manifold", "pseudoscalar", and "spac …
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10 votes
4 answers
1k views

Moduli spaces in applied mathematics and condensed matter physics?

In this MO question it is stated that there is a relation between some aspects of condensed matter physics (namely the fractional quantum Hall effect) and the algebraic geometry of Hilbert schemes. H …
126 votes
15 answers
15k views

Does Physics need non-analytic smooth functions?

Observing the behaviour of a few physicists "in nature", I had the impression that among the mathematical tools they use a lot (along with possibly much more sofisticated maths, of course), there is c …
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  • 23.4k
3 votes
0 answers
248 views

Velocity field of fluid and Maurer-Cartan form?

Chatting with an engineer, he suggested me to have a look to a certain book in order to understand what fluid mechanics is about (I know nothing about the subject). But this question is not about flu …
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  • 23.4k
21 votes
5 answers
2k views

Is there a relation between 4-dimensional general relativity and exotic smooth structures on...

Let's say General Relativity is the study of the Einstein equation on smooth Lorentzian manifolds, i.e. pseudo-Riemannian manifolds of signature $(n-1,1)$. I've heard more than once people say that th …
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  • 23.4k
3 votes
0 answers
247 views

Brachistochrones on Riemannian manifolds

Let $(M,g,V)$ be a Riemannian manifold with potential $V\in\mathcal{C}^{\infty}(M)$. Let $\gamma : I\to M$ be a smooth curve, $I\subseteq \mathbb{R}$ an open interval. We say that $\gamma$ is the traj …
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  • 23.4k
47 votes
11 answers
15k views

Standard model of particle physics for mathematicians

If a mathematician who doesn't know much about the physicist's jargon and conventions had the curiosity to learn how the so called Standard Model (of particle physics, including SUSY) works, where sho …