Mathjax Test

The formulas in the header.

$$\begin{array}{rl}[{\mathcal{L}}_{\xi },{\mathcal{L}}_{\eta }]& ={\mathcal{L}}_{[\xi ,\eta ]}+\frac{1}{2\pi i}\int dt{\dot{q}}^{\rho }(t)(c_1{\partial }_{\rho }{\partial }_{\nu }{\xi }^{\mu }(q(t)){\partial }_{\mu }{\eta }^{\nu }(q(t))+\\ & +c_2{\partial }_{\rho }{\partial }_{\mu }{\xi }^{\mu }(q(t)){\partial }_{\nu }{\eta }^{\nu }(q(t))),\\ [{\mathcal{L}}_{\xi },q^{\mu }(t)]& ={\xi }^{\mu }(q(t)),\\ [q^{\mu }(t),q^{\nu }(t^{\prime })]& =0.\end{array}$$

If you use Firefox with NoScript, as I do, you need to whitelist jsdelivr.net and polyfill.io, otherwise only the uncompiled LaTex code will show up.

If anybody wonders, this is the Virasoro-like extension of the diffeomorphism algebra in multiple dimensions. e.g. on the $d$-dimensional torus. When $d=1$, both terms proportional to $c_1$ and $c_2$ reduce to the ordinary Virasoro algebra on the circle, a piece of mathematics that is popular e.g. in string theory and statistical physics. By the way, I discovered the $c_2$ term myself a long time ago, which is something that I am still proud of ($c_1$ was discovered by Rao and Moody).

When I started this blog almost a decade ago I had planned to write about this and how it in my opinion fits into physics, hence the name of the blog. I never got around to do that, but that might change in the future.