9
votes
Is Norton's dome valid (or does $\frac{d^2 \vec{p}}{dt^2} = \vec{0} \implies \frac{d^n \vec{p}}{dt^n} = \vec{0} \ \forall \ n > 2$)?
Your example is not analogous to Norton's dome.
Norton's point is that Newtonian mechanics says that the trajectory of a particle obeys $\ddot{x}(t) = F(x(t),\dot{x}(t), t)$ at every point in time $t$,...
- 107k
2
votes
Permanent magnets - why spontaneous symmetry breaking?
First I will write some general remarks about spontaneous appearance of orientation. After that I go to the question specifically.
Take the following demonstration:
Take a large plate, in the middle ...
- 15.4k
2
votes
Accepted
What were the $r$ and $n$ of $\theta$s (Polchinski String theory section 8.6 page 265)?
The numbers $r_i\in\mathbb{N}$ are the degeneracies/multiplicies of the eigenvalues $\theta_i$ of the diagonal background gauge field $A_{25}$ in the compactified 25th direction
$$ A_{25}~=~-\frac{1}{...
- 170k
1
vote
Nonlinear symmetry realization: what is it for and caveats?
$\newcommand{\ex}[1]{\mathrm{e}^{#1}}\newcommand{\i}{\mathrm{i}}$Let me add a couple of points to Cosmas' answer
A crucial observation for your first question is that
\begin{align}
[X_\alpha,X_\beta] ...
- 1,718
Only top scored, non community-wiki answers of a minimum length are eligible