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Let $\psi\colon\mathbb R\to\mathbb C$, and set $$ F[\psi]:=\pi\ \frac{\displaystyle\int_{\mathbb R} |x|\;|\psi(x)|^2\,\mathrm dx}{\displaystyle\int_{\mathbb R}|\psi(x)|^2\,\mathrm dx}\frac{\displaysty …

I posted this question to physics.SE last week (cf. here), but it got not attention. I hope it is not too trivial to post it here. According to ref.1, the correlation functions of a Chern-Simons theo …

Here is a very simple Lagrangian that yields the Maxwell equations upon variation, taken from this post (also by me) on physics.SE. The trick is to introduce Lagrange multipliers. Let \begin{equation} …

Physicists here. The input for a physical theory is always some topological space and some structure (such as a metric) that depends on the specific context. The dynamics are invariant under the isome …

Use $$ [\nabla_\mu,\nabla_\nu]V^\rho=R_{\mu\nu}{}^{\rho\sigma} V_\sigma $$ to conclude that $$ \begin{aligned} {}[\nabla^\nu\nabla_\nu,\nabla_\mu]\phi&\overset{ \mathrm A}=\nabla^\nu[\nabla_\nu,\nabla …

Note that the Schrödinger action, say in flat space-time, $$ S=\int\mathrm dx\ \psi^*\left(i\frac{\mathrm d}{\mathrm dt}+\frac{1}{2m}\nabla^2\right)\psi $$ has a length scale (mass) $m$, and yet it is …

This is a refinement of this old question of mine. In order to find an answer, I've been working my way through q-alg/9511026, which contains all the information I need. In this paper, the authors as …

See §15 in Dictionary on Lie Superalgebras, by L. Frappat, A. Sciarrino, P. Sorba. They define the Dynkin diagram of basic Lie superalgebras (i.e., those with an even nondegenerate invariant bilinear …

Assume I successfully classified the integrable representations of a certain semi-simple Lie group $G$. Given this information, what do I know about the integrable representations of $G^\vee$, the Lan …

He${}$llo MO. Let $\mathrm{O}(n_1,n_2)$ be the pseudo-orthogonal group. I am interested in its (continuous, not necessarily unitary, finite-dimensional) irreducible projective representations, for ar …