Current algebra
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Current algebra is a technique in quantum field theory where the fields form a Lie algebra under their commutation relations.
For instance, if we have a non-Abelian Yang-Mills symmetry, and ρ is the charge density, then
![[\rho^a(\vec{x}),\rho^b(\vec{y})]=if^{ab}_c\delta(\vec{x}-\vec{y})\rho^c(\vec{x})](../../../math/6/a/a/6aaa46f28d7c10f2f6cd77a0ce83e141.png)
where f are the structure constants of the Lie algebra. If space is a one dimensional circle, we may have central extensions.
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