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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.

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51 views

### Functional calculus problem : how “similar” are the position operator and generator of dilations?

The context is that of discrete Schr"odinger operators. We work in the Hilbert space $\ell^2(\mathbb{Z})$. $S$ and $S^*$ denote the shift operators on the lattice $\mathbb{Z}$ respectively to the ...
1answer
73 views

### PDE's : diffusion equation : polynomial diffusion coefficient

I'd like to find analytical solutions of that kind of differential equations : $$\partial_t c = \partial_x (D(c)\partial_x c)$$ with $D(c)$ a polynomial. The trivial cas $D(c)=a$ with $a$ a ...
2answers
858 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 ...
1answer
136 views

### Jack polynomial and Selberg integral

I am studying the generalisation of the Selberg's integral by using Jack polynomial as outlined by Forrester and Warnaar (arXiv: 0710.3981). They write down the symmetric Jack polynomial as \begin{...
0answers
198 views

### The use of Schur's lemma for Lie algebras in physics (CFT)

Anytime a one-dimensional central extension appears in the physics literature, immediately they assume that in any irreducible representation the central charge will be a multiple of the identity, ...
1answer
471 views

### Physicists misuse the term “Kac Moody algebra”. Does that bring problems?

In physics textbooks one frequently sees the name (affine) Kac Moody algebra used to describe the universal (one dimensional) central extension of the loop algebra of a semisimple algebra. But this is ...
0answers
73 views

### Branching rules for E6 into SU(3)^3

I am very confused about what are the branching rules for representations of $E6$ into a $SU(3)\times SU(3)\times SU(3)$ subgroup. At least in the physics literature, there seems to be a serious ...
1answer
85 views

### Generalized Fourier integral and steepest descent path, saddle point near the endpoints

I am looking forward to solving the integration in the following equation with the assumption that $ka$ is very large \begin{align} H = 2jka\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{jka[\cos{\...
1answer
454 views

### Are there currently any plausible approaches to proving the Penrose сonjecture?

I have recently been reading some of the literature on the Penrose inequality, especially the papers by Bray and by Huisken and Ilmanen. One notices immediately that the existing proofs for the ...
1answer
520 views

### Natural examples of $(\infty,n)$-categories for large $n$

In Higher Topos Theory, Lurie argues that the coherence diagrams for fully weak $n$-categories with $n>2$ are 'so complicated as to be essentially unusable', before mentioning that several dramatic ...
1answer
94 views

### What fraction of a charge is induced on a surface via balayage?

Consider a smooth, bounded domain $\Omega \subset \mathbb{R}^3$, and place a charge $q>0$ at a point $z\in\mathbb{R}^3\setminus\overline\Omega$. Via the concept of balayage, there is an induced ...
0answers
91 views

### non-associative deformation quantization [closed]

Several physicists now consider non-Poisson bivectors but still apply Maxim’s morphism for deformation quantization. The result is a `non-associative star product’, So a deformation as a ________? ...
0answers
92 views

### Are all cellular automata models related to the Bekenstein bound and the holographic principle?

Cellular automata are discrete models which have a regular finite dimensional grid of cells, each in one of a finite number of states, such as on and off. There are various scientists that have ...
1answer
92 views

### What are the topological phases of quantum Hall systems?

(Fractional) quantum Hall systems are $2+1$-dimensional models which are said to possess topological order. One (maybe even complete) set of invariants of topological phases in $2+1$ dimensions is ...
1answer
126 views

### Knizhnik-Zamolodchikov equation is a connection on “affine slice”

The question is - what is the precise meaning of the phrase in the title? I heard it from Andrey Okounkov during one of his lectures. The problem is that he didn't really specified which slice is ...

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