# Tagged Questions

In mathematics, topology examines the properties of space (such as connectedness and compactness) that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing.

47 views

### The expansion of the universe and its edge

I have understood that the universe is expanding at an accelerated rate. I have also thought, perhaps mistakenly, that this expansion means not that the masses in the universe are moving away from ...
12 views

### How does a position based force work on a torus?

Consider a 2 particle system in $\Bbb R^2$. Let's say they have some force acting between them. For the sake of argument let that be $F=\mathbf r/|\mathbf r|^3$. This is a simple inverse square system ...
76 views

### Yang-Mills potential and principal bundles

In section 2.7.2 of Bertlmann's "Anomalies in quantum field theory", it is stated that since a non-trivial principal bundle (based on a Lie group $G$) does not admit a global section, the Yang-Mills ...
45 views

### Relation between projective representations, connectivity of a group manifold and number of equivalence classes of paths

Projective representations of a multiply-connected group is defined as $$U(g_1)U(g_2)=c(g_1,g_2)U(g_1g_2)$$ where $c(g_1,g_2)$ is phase. Reading various articles, and this old post of mine, it appears ...
49 views

### Lorentz surfaces, conformal metrics and eigenvalues

From what I understand of Lorentz surfaces (spacetimes of dimension 2), it seems that, according to Kulkarni's theorem, two reasonable enough Lorentz surfaces (I am only interested in surfaces with ...
26 views

### Wave equation for odd spacetimes and source terms

It seems to be quite common practice, when solving the wave equation in spacetimes with odd topologies or horizons, to decompose the solution into a sum of the various origins (or destinations) of the ...
From Ex 3.1 in the TASI lectures on the conformal bootstrap: http://arxiv.org/abs/1602.07982 the problem is the inversion map (with Euclidean signature) $$I\colon x^\mu \mapsto \frac{x^\mu}{x^2}$$ ...