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 $t$,...
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  • 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 ...
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2 votes

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}{...
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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] ...
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