# 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,

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

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