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In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!
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Free-Field Construction of the Virasoro Algebra
The Virasoro algebra is given by the relation
$$
[L_m, L_n] = (m-n)L_{m+n} + \frac{c}{12}m(m^2 -1)\delta_{m,-n}.
$$
Also consider a free spin-1 field in 1+1 dimensions (which is invariant under confor …