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# Questions tagged [mp.mathematical-physics]

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

1,407 questions
1answer
821 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 ...
0answers
96 views

### Conjecture for a certain Cauchy-type determinant

Given the Cauchy-like matrix  \mathbf X_M(q) = \left[ \frac{2}{\pi} \frac{ \Gamma\!\left(m - \frac{1}{2} \right)\Gamma\!\left(n + \frac{1}{2} \right) }{ \Gamma(m)\,\Gamma(n) } \frac{m-\frac{3}{4}} {\...
0answers
49 views

### What is the best book to learn about the wave equation? [closed]

I'm looking for a book that teaches the wave equation and how to solve it for more advanced cases than the basic one (infinite/half infinite string, standing waves etc) What book would you recommend ...
0answers
64 views

### Surfaces extending modified geodesic paths

What happens if the usual geodesic equation on an n-manifold is directly modified from a source dimension 1 space (giving a path) to a dimension 2 space (giving a surface). I suspect that this gives a ...
1answer
154 views

### Definition of a Dirac operator

So it seems that a Dirac operator acting on spinors on $\psi=\psi(\mathfrak{su}(2),\mathbb{C}^2)$ can be written in this case simply as: $D=\sum_{i,j} E_{ij}\otimes e_{ji}$, where $E_{ij}$ are ...
1answer
78 views

### Localization of solutions for time-dependent Schroedinger equation

I've been playing around with numerical solutions to the Schroedinger equation and I came across something that feels very natural, but I was not able to prove it with the math I know. The ...
0answers
74 views

### Decomposition of the group of Bogoliubov transformations

Consider the fermion Fock space $\mathcal{F}=\bigoplus_{k\ge 0}\bigwedge^k\mathfrak{h}$ of some finite-dimensional 1-particle Hilbert space $\mathfrak{h}$. The group $\mathrm{Bog}(\mathcal{F})$ of ...
2answers
122 views

0answers
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### How to choose phase to give a desired Fourier transform

Cross posted from MSE. I have a mathematical problem arising from a physics application, which I feel must have been solved before, but I don't know the terminology associated with it. I am looking ...

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