# Tagged Questions

**2**

votes

**2**answers

202 views

### In what condition is a conformal flat manifold flat?

$g^{\mu\nu}(x)=\Omega^{2}(x)g'^{\mu\nu}(x)$ is a conformal transformation.
If $g'^{\mu\nu}$ is flat, what kind of $\Omega(x)$ is choosed can make $g^{\mu\nu}$ flat.
We can think about any dimension ...

**2**

votes

**0**answers

130 views

### What are Euler density and Weyl invariants?

I would like to know as to what is the definition and significance of what are called "Euler density" and "Weyl invariants" (of weight $-d$ on a $d-$manifold)
Do many (which?) of them vanish when ...

**1**

vote

**1**answer

172 views

### Analytic curve on Riemann surface

Suppose there is a closed analytic curve $C$ on a Riemann surface $S$, that is the image of a map $\gamma$ from the equator $E$ of the Riemann sphere to the surface $S$ which is a restriction of a ...

**3**

votes

**1**answer

333 views

### eigenspinors of Dirac operator

$M$ compact manifold. Let $\lambda$ be an eigenvalue for the Dirac operator of multiplicity greater than 2. I'm interested in showing the existence of two linearly independant eigenspinors $u$ and $v$ ...

**4**

votes

**0**answers

332 views

### Correlation functions of complex operators

One defines the "scaling dimension" (as opposed to "engineering dimension") of an operator $\cal{O}$ as $[\cal{O}]$ such that if $\cal{O}(t^{-1}x) = t^{[\cal{O}]}\cal{O}(x)$ then the Lagrangian in ...

**2**

votes

**0**answers

283 views

### Collection of charged line segments in 2D - where do electric field lines meet it?

Suppose we have a collection of charged line segments in 2D. I'd like to be able to do two things :
from an arbitrary point in the plane, follow the electric field and find where it meets the ...