# Tag Info

Accepted

### Is the electroweak gauge group a semidirect product?

Note that the group monomorphism $$U(1)_Q\quad \stackrel{i}{\hookrightarrow}\quad G~:=~ N\times U(1)_Y, \qquad N~:=~SU(2)_I,$$ depends on the Weinberg angle, cf. e.g. my Phys.SE answer here. Here the ...
1 vote
Accepted

### What does really mean to glue the endpoints of a closed string?

The equivalence relation $\sigma\sim\sigma+2\pi$ is just constructing a circle for you: $\mathbb{S}^1 \cong \mathbb{R}/2\pi\mathbb{Z}$. Instead of using the equivalence class $[\sigma]$ we use a ...
Accepted

Accepted

### Gauge transformation as transition functions?

The same way you can locally view diffeomorphisms as coordinate changes. Let $\pi: P\rightarrow M$ be a principal $G$-bundle. As it is well-known, for a PFB, local trivializations and local sections ...
1 vote

### How is a wormhole (Einstein-Rosen Bridge) different than a tunnel?

While a tunnel in mountain is a "hole" in matter, a wormhole is a "hole" in fabric of spacetime. Although spacetime and matter are closely related via equations of general ...

### In what way are Lie groups generated by the basis of their Lie algebra?

Maybe as a simple example, consider $O(2)$ (real $2\times 2$ matrices $M$ with $M^T M=\mathbb{1}$). You can see that $\det M=\pm1$, so the group is disconnected (you cannot have a continuous path from ...
The main points are that given a Lie group $G$, the Lie algebra $\mathfrak{g}=T_eG$ is the tangent space of the identity element $e\in G$. generators are a basis for the Lie algebra $\mathfrak{g}$. ...