Current algebra

Current algebra is a mathematical framework in quantum field theory where the fields form a Lie algebra under their commutation relations.

For instance, in a non-Abelian Yang–Mills symmetry, where ρ is the charge density,

[\rho^a(\vec{x}),\rho^b(\vec{y})]=if^{ab}_c\delta(\vec{x}-\vec{y})\rho^c(\vec{x})

where f are the structure constants of the Lie algebra. If space is a one-dimensional circle, there may exist central extensions.

See also

References