# Tagged Questions

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

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### Dropping three bodies

Consider the usual three-body problem with Newtonian $1/r^2$ force between masses. Let the three masses start off at rest, and not collinear. Then they will become collinear a finite time ...
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### Correspondence between eigenvalue distributions of random unitary and random orthogonal matrices

In the course of a physics problem (arXiv:1206.6687), I stumbled on a curious correspondence between the eigenvalue distributions of the matrix product $U\bar{U}$, with $U$ a random unitary matrix and ...
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### Infinitely many planets on a line, with Newtonian gravity

(I previously asked essentially this on physics.stackexchange, but was actually hoping for answers with something closer to a proof than what I got there.) Suppose we have a unit mass planet at each ...
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### Catalan objects associated to a univariate polynomial

Given a monic degree $n$ polynomial $f(z)$ with no double roots, and a phase $0\leq \theta < \pi$, there are natural constructions which associate to this data: a noncrossing matching on $2n$ ...
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### Which limit to take as a key applied math decision

The Borel-Kolmogorov paradox refers to situations where non-uniqueness in the notion of conditioning on a set of measure zero leads to apparent contradictions. As a formal matter, one requires ...
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### Squeezing physics out of formal deformation quantizations

I am reading various texts concerning the concept of "quantization". I am interested in quantization on Riemannian manifolds (as opposed to just on $\Bbb R ^n$); for absolute clarity, I am interested ...
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### “extended TQFT” versus “TQFT with defects”

There are two ways in which higher categories appear in topological field theory: in extended TFTs and in TFTs with defects. How are these appearances related? According to the Atiyah-Segal axioms, a ...
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### conformal blocks for beginners

I have given now a couple of talks that involve conformal blocks bundles on the moduli stack $\overline{\mathcal{M}}_{g,n}$, in front of a public of algebraic geometers but not specialists of the ...
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### Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise: What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if ...
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### What is known about the Yang-Mills stratification over 3-manifolds?

Rade proved in his thesis (Crelle's Journal, 1992, available here: digizeitschriften.de/dms/toc/?PPN=PPN243919689) that if $E\rightarrow M$ is a $U(n)$-bundle over a 3-manifold, then the gradient flow ...
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### What is the symmetry group fixing norms of elements of a unitary matrix?

Let $N\geq1$ be an integer and let us say that two matrices $U,V\in U(N)$ are related if $|U_{ij}|=|V_{ij}|$ for all indices $1\leq i,j\leq N$. When exactly are two unitary matrices related in this ...
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### State of the art of BPS and Donaldson-Thomas invariants for toric Calabi-Yau threefolds

I am trying to understand what has been done with regards to computing BPS invariants and Donaldson-Thomas type invariants of Calabi-Yau threefolds. To make the question more focused, let's say that I ...
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### The open problem of nth quantization

In trying to explain a quote by E. Nelson, "First quantization is a mystery, but second quantization is a functor!" Baez points out what follows (full text available in this week find; I'm also ...
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### Parametrisations for Null Temperature Functions: nonuniqueness of solutions to the Heat Equation

Disclaimer I expect this is a highly open problem, but maybe I'm wrong and someone has come up with some answers besides those given here. In any case, all information appreciated, thanks! Definition ...
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### Curvature as infinitesimal holonomy

Let $P \to M$ be a principal $G$-bundle, assume as much regularity as you want (compact $G$ or compact base manifold, ect). Via parallel transport, a connection $A$ on $P$ gives rise to the holonomy ...
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### Equivariant quantum cohomology and K-theory of vector bundles over a Grassmannian

Consider a sum of m copies of the tautological bundle over the Grassmannian of n-planes in complex k-dimensional vector space. There is an obvious action of an (m+k)-dimensional torus T on the total ...
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### triangulated/derived categories in Physics and algebraic geometry

Why do physicists care about the triangulated/derived categories? I mean what are the problems we want to approach using the machinery of triangulated/derived categories. e.g. in homological mirror ...
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### Modular Tensor Categories: Reasoning behind the axioms

(Sorry for the length of the question, I'm trying to communicate what is bothering me as thoroughly as possible) In the construction of modular tensor categories (MTC) from ground zero, we put ...
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### Flat connection from gauged WZW model

$\newcommand{\g}{\mathfrak g}$ $\newcommand{\h}{\mathfrak h}$ In short my question is : Has someone worked out the flat connection that one should get from the gauged WZW model in genus 0 ? Some ...
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### Question about theorem in Arnold's book on action-angles variables

I have a question about the action-angle theorem on p. 283 in Arnold's textbook on classical mechanics.(I added the link to this book in the last part of this question) If you don't have the book or ...
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### Characterize spin cobordism invariants in dimer models

The paper by Cimasoni and Reshetikhin http://arxiv.org/abs/math-ph/0608070 shows that one can map problems about spin structures on a Riemann surface into problems about dimmer configurations on a ...
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### Explicit expression of WZ term for orthogonal groups

Consider the Wess Zumino term on the the space $W=I\times D$, where D is a two dimensional disk disk and $I$ is an interval, $[0,1]$, say, i.e., $$\int_{I\times D} \langle(u^{-1} \, du)^3\rangle$$ ...
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### Deformation of Noether's first theorem

Noether's first variational theorem establishes a correspondence between symmetries and invariants. I would like to know what has been written on the following question: How do the invariants deform ...
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### Chern-Simons form and Rarita-Schwinger operator

The Rarita-Schwinger (RS) operator naturally generalizes the Dirac operator and in Physics it describes particles with spin-3/2. I was wondering if there exists any reference concerning the ...
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### intuitive connection between The KdV equations and the Virasoro bott group

I posted this on stack exchange but had no joy, perhaps someone here can answer : The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group....
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### Reference for supergroupoids in supersymmetry?

I would like to know some references on supergroupoids in supersymmetry. A supersymmetry is invariance under a supergroup action (nLab, Supersymmetry). It is know that groupoids provide a local ...
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### Extreme unitary minimal models of conformal field theory

Some of the best understood conformal field theories are the 2D unitary minimal models $\mathcal{M}(m+1,m)$ indexed by the integer $m\ge 2$ and with central charge $$c=1-\frac{6}{m(m+1)}\ .$$ I ...
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### Can one classify irreducible unitary representations of the Weyl algebra?

I saw in this MO post: Is there a machinery describing all the irreducible representations ? that classifying irreducible representations of the Weyl algebra is essentially intractable. My question is ...
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### Density of odd and even eigenstates of an integral operator

Consider an integral operator $(Kf)(x)=\int_{-1}^{1}K(x-y)f(y)dy$, where the kernel $K(-x)=K(x)$ is an even function. Let $\lambda_n$ be the ordered eigenvalues of $K$ and $f_n(x)$ the ...
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### Spectral theory for Dirac Laplacian on a funnel

I would like to study the spectral theory of the Dirac Laplacian on a non-compact quotient of the hyperbolic plane by a discrete group (I am particularly interested in the simple case where the ...
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### Would a closed universe with special relativity violate causality? Does the universe have to be simply connected?

This question may be more appropriate for physics.stackexchange.com, but it would be helpful to get feedback from experts in Minkowski geometry. The classic twin paradox is a false thought experiment ...
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### Birth-Death Process associated with Orthogonal Polynomials

I have read in various places the following objects are related: orthogonal polynomials birth-death processes Lattice paths continued fractions After a lot of searching online, I found sketches ...
Consider locally minimizing harmonic maps from D-dimensional Euclidean space into a compact Lie group G. When $D=3$ the general regularity theory due to Schoen-Uhlenbeck, Schoen, Richard; Uhlenbeck, ...