**17**

votes

**2**answers

774 views

### How does hyperbolicity of space time affect our lives?

My main research has been in hyperbolic geometry and geometric group theory. I always thought that the only real "application" of my work was that the universe is a 3-manifold.
But recently I found ...

**1**

vote

**2**answers

302 views

### Translation of an article

I need to read this article
"On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups"
authors:G.Zhislin, A. ...

**2**

votes

**0**answers

113 views

### universal connection for SU(3)

In 1961, Narasimhan and Ramanan (Am J Math 83 563) showed that one could represent an arbitrary SU(3) connection as $ i t^c_{a b} A^c_\mu(x) = e^*_a \cdot e_{b, \mu}(x) $ in which the $ t^a $'s are ...

**2**

votes

**0**answers

101 views

### Three body problem with two fermions and a different particle

I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows them?

**1**

vote

**1**answer

350 views

### maxwell's equations and hodge theory

How is Hodge theory of harmonic forms related to maxwell's equations.Atiyah says that Hodge was directly motivated by considerations of maxwell's equations while commenting on donaldson.

**1**

vote

**1**answer

180 views

### Gaussian measures on non-separable spaces

Let $X$ be a topological affine space which is neither separable nor metrizable. There are plenty of trivial Gaussian measures: each Dirac point-mass $\delta_x$ are the Gaussian measure with zero ...

**1**

vote

**0**answers

173 views

### Is connected correlation/cumulant expansion additive?

Say X is a free field or a Gaussian random variable.
Then I want to analyse the connected correlation, $<(X + a (X^2 - \langle X^2 \rangle))^n>_c$
I think that for $n \geq 4$ there are no ...

**1**

vote

**0**answers

128 views

### Self Dual 2-Forms on Complexified Minkowski Space

I'm trying to get my head around integrability in twistor theory, but am struggling with interpreting the concept of self-duality on complexified spaces.
One can complexify Minkowski space to ...

**3**

votes

**1**answer

221 views

### Solvable models in quantum mechanics

Is there anyone who studied on the book "Solvable Models In Quantum Mechanics" by Albeverio? I don't succed in understanding the proof of page 116 about the eigenvalues of the Hamiltonian with point ...

**1**

vote

**2**answers

213 views

### The limiting behavior of geometric random walk

I would like to know what the asymptotic limiting behavior is for the following random walk on $\mathbb Z^d$. By Donsker's invariance principle, I suspect that its behavior is diffusive, i.e., the ...

**1**

vote

**1**answer

361 views

### Wedge Product of Lie Algebra Valued One-Form

I've been reading about the formal structure of gauge theories and am a little confused by the notation. Could someone clarify this for me?
Suppose that $A$ is a Lie algebra valued 1-form ...

**1**

vote

**3**answers

341 views

### Explicit model of BSU(2) in terms of singular complex

What is the explicit model of BSU(2) in terms of singular complex, up to 5 dimensions,
so that one can compute $\pi_5(BSU(2))=\mathbb{Z}_2$ explicitly?
This question is related to another question of ...

**1**

vote

**1**answer

296 views

### $\pi$-cohomology class — a variant of cohomology class

Let $X$ be a topological space with a triangulation. The triangulation defines a
chain complex in $X$. Let $\mu_d$ be a cochain and $M^d$ be a chain. We use $<
\mu_d, M^d > \in M$ to denote ...

**1**

vote

**3**answers

183 views

### Applied examples of (non)uniformly hyperbolic and/or ergodic systems

I try to give reference to completely applied examples of (non)uniformly hyperbolic and/or ergodic systems. With completely applied I don't mean an irrational rotation on the torus but from other ...

**1**

vote

**0**answers

153 views

### multivalued solution of a equation

Definition: A scalar k-th order differential equation on a smooth manifold $M$ ,
is $F(x,v,\frac{\partial {^\left | \sigma \right |}v}{\partial x^\sigma })=0 $
for $\left | \sigma \right |\leqslant ...

**5**

votes

**1**answer

187 views

### Linearization instability and singular points of algebraic varieties

In a well known 1973 paper, Fischer and Marsden pointed out (with similar, contemporary remarks made in the physics literature by Brill and Deser) that the space of solutions of some non-linear ...

**3**

votes

**0**answers

95 views

### Lower bounds of laplace transform of characteristic functions

Cross-posted on maths.stackexchange
I have the following integral:
\begin{equation}
f(\mu) = \int_0^\infty e^{-\mu t}\varphi_X(t)dt
\end{equation}
where $\varphi_X(t)$ is the characteristic function ...

**8**

votes

**1**answer

547 views

### What is quantum Brownian motion?

It seems that the current state of quantum Brownian motion is ill-defined. The best survey I can find is this one by László Erdös, but the closest the quantum Brownian motion comes to appearing is in ...

**0**

votes

**0**answers

261 views

### Moment of Inertia of a Polygon

I'm programming a game and I have to find the moment of inertia of a flat polygon (axis of rotation is perpendicular to the polygon, from now on I will call it the point of rotation). My idea was to ...

**0**

votes

**1**answer

274 views

### From Brownian Motion to the Heat Equation

Consider a set of N balls that start at the origin. In a given unit of time, $\delta t$, the balls have a probability $p = 0.5$ of jumping a distance $\delta x$ to the right, and the same probability ...

**0**

votes

**0**answers

374 views

### Solving a linear recurrence relation with variable coefficients.

I have the following recurrence relation:
\begin{equation}
A[n]=f_A[n-1] A[n-1] + f_B[n-1]B[n-1], \\
B[n]=g_A[n-1] A[n-1] + g_B[n-1]B[n-1],
\end{equation}
where ...

**5**

votes

**0**answers

149 views

### Given that a conditional measure is Gaussian, how bad can the original measure be?

Let $X$ and $Y$ be Banach spaces, and let $\varphi : X \to Y$ be a continuous linear map. Suppose that $\mathbb P$ is a probability measure on $X$ which satisfies the continuous disintegration ...

**4**

votes

**2**answers

779 views

### Eigenvalues of random Hamiltonian matrices

A real $2n\times 2n$ Hamiltonian matrix has the general form
$$H=\begin{pmatrix}
A & B \cr
C & -A^T
\end{pmatrix}
$$
where $A$, $B$ and $C$ are $n\times n$ matrices, and $B$ and $C$ are ...

**7**

votes

**1**answer

365 views

### necessary and sufficient condition for existence of $SU(3)$-structure on 6-manifolds

Is there any necessary and sufficient condition for existence of $SU(3)$-structure on 6-manifolds $M$?

**8**

votes

**2**answers

394 views

### Is the quantum algebra unique (up to isomorphism) in deformation quantization ?

Consider a Poisson algebra A (i.e. commutative algebra with Poisson bracket).
Let $\hat A$ be a deformation quantization of the algebra A. We know that construction of deformation quantization and ...

**0**

votes

**1**answer

329 views

### The real and imaginary parts of the Incomplete Gamma function for second argument being purely imaginary

Dear all,
I am looking for explicit (at least more explicit than the original expression) for
1) Re$(\Gamma(a, i\omega))$
as well as
2) Im$(\Gamma(a, i\omega)),$
where i Re and Im denote the real ...

**6**

votes

**7**answers

589 views

### Quantization of a classical system (e.g. the case of a billard)

There has been already several questions asking for an introduction to quantum mechanics
for a mathematician, but this ons is slightly different, and more restrictive. I know (some)
quantum mechanics, ...

**3**

votes

**1**answer

140 views

### Second quantization of partial isometry

If we have a unitary map from Hilbert space $H$ to $H$, we get a unitary map from $e^{H}$ to
$e^{H}$, where $e^{H}$ is the symmetric Fock space of $H$. But if we replace the unitary with partial ...

**0**

votes

**0**answers

104 views

### What is the integer form of a projector into the intersection of the ranges of two integer projection matrices?

Consider two square integer matrices $X$ and $Y$ of the same dimension with the following properties:
$X^2=rX$, and $Y^2=sY$ for integers $r$ and $s$. The $\gcd$ of the entries of $X$ is 1 and the ...

**2**

votes

**2**answers

414 views

**10**

votes

**1**answer

777 views

### decompositions for exceptional Lie algebras $E_6$, $E_7$ and $E_8$

Do anybody know , why can we write the following decompositions for exceptional Lie algebras $E_6$, $E_7$ and $E_8$
1) $E_8=(V^{\star}\otimes \wedge^{8}V^{\star})\bigoplus ...

**6**

votes

**1**answer

285 views

### Relation between TQFT and Wilson lines, boundary conditions, surface defects etc

I have been studying (extended) topological quantum field theories (in short TQFTs) from the mathematical point of view and I have no background of the physics point of view. Sometimes I encountered ...

**2**

votes

**1**answer

406 views

### why the group $GL(6,V)$ has an open orbit?

N.Hitchen in his paper about geometry of three forms wrote that "for a Real vector space $V$ of dimension six, the group $GL(6,V)$ has an open orbit and he referenced it to a thesis which was written ...

**11**

votes

**2**answers

734 views

### Hopf Algebra for a physicist

Hello,
for my bachelor's thesis I need to understand the Hopf Algebra of Feynman Diagrams. As I have only litte knowledge in Algebra by now I wanted to ask where I could start and what preknowledge I ...

**4**

votes

**3**answers

581 views

### Meaning of a phrase from “The algebra of grand unified theories”.

Motivated by an answer to this mathoverflow question I've been making an effort to understand Baez and Huerta's article "The algebra of grand unified theories".
As far as I can tell, mathematically, ...

**10**

votes

**0**answers

304 views

### 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 ...

**11**

votes

**2**answers

506 views

### What do correlation functions compute in CFT?

I would like to understand what correlation functions compute in Conformal Field Theory in mathematics. Let me begin with basic definitions. We define a free boson field $\phi(z)$ as a formal power ...

**5**

votes

**2**answers

388 views

### Permuting Racked Pool Balls with a Single Break

Given reasonable physical assumptions (on friction, collisions, etc.), would it be possible to "break" in a pool game such that when all the balls come to rest, the only difference is that the racked ...

**4**

votes

**1**answer

191 views

### Rotations, Harmonic Oscillators, Gaussians, Ladders

I am trying to understand better the quantization of the Harmonic Oscillator.
Here are three ways of thinking about the Harmonic Oscillator.
Eigenfunctions of the differential operator: $H = ...

**6**

votes

**2**answers

398 views

### When is a space of measures a measurable space?

Let $X$ denote a measurable space, that is, a set equipped with a $\sigma$-algebra $\Sigma(X)$. Let $M(X)$ denote the space of real-valued measures over $X$. This is a vector space over the real ...

**0**

votes

**0**answers

77 views

### Divisors, factorisations of matrix valued functions, and the Lorentz group

How to construct a complex projective variety with several classes of non-intersecting divisors? How to keep the answer concrete and simple, so that explicit calculations can be done? And the problem ...

**2**

votes

**2**answers

399 views

### An interesting equation of some practical interest.

I have encountered a problem in my elec. eng research that I find rather challenging, being a bear of very little brain. The question has been considered under a slightly different aspect here: ...

**8**

votes

**3**answers

465 views

### Space of sections of a fibre bundle with non-compact base space

Let $\pi: E \rightarrow M$ be a fiber bundle over the manifold M and denote by $\Gamma(E)$ the space of smooth sections of $E$.
For compact $M$ it is well known (Hamilton 1982, Part II Corollary ...

**31**

votes

**7**answers

3k views

### The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?

Starting from 80-ies the ideas either coming from physics, or by physicists themselves (e.g. Witten) are shaping many directions in mathematics. It is tempting to paraphrase E. Wigner, saying about ...

**4**

votes

**0**answers

414 views

### Open question: non-commutative site following Grothendieck, Quillen, Connes and Crane for quantum gravity.

This is an open question and it's to find out who is interested in this kind of thing, who can benefit from thinking about this. It is very brief but hopefully will only be unclear to people who are ...

**19**

votes

**6**answers

2k views

### Mathematician trying to learn string theory

I'm a mathematician. I want to be able to read recent ArXiv postings on high energy physics theory (String theory) (and perhaps be able to do research). I want to understand compactifications, ...

**0**

votes

**1**answer

88 views

### orthotropic materials solution of boundary value problems

What are the methods or approaches for the analytical solutions of boundary value problems in the theory of elasticity for orthotropic materials?

**10**

votes

**1**answer

330 views

### What are the simple Lie superalgebras of type E?

Background
Simple finite dimensional Lie superalgebras over $\Bbb C$ have been classified. There are the Cartan type superalgebras (algebras of purely odd vector fields), two strange families P(n) ...

**1**

vote

**1**answer

234 views

### Why $O(4n,\mathbb{C})$ (orthogonal group) acts transitively on the space of maximal isotropics of $V\bigotimes \mathbb{C}$ ?

We say $L< (V\oplus V^{*})\bigotimes \mathbb{C}$ is isotropic when $< X,Y>=0$ for all $X,Y\in L$
Why $O(4n,\mathbb{C})$ (orthogonal group) acts transitively on the space of maximal ...

**0**

votes

**0**answers

107 views

### Is there “harmonic potential” for classical bosonic string?

I am sorry that I did not sound understandable in my pervious questions.
There is a stringy version i.e. categorical version of the classical (non-quantum) physics situation in which a test massive ...