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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,

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

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

See also

• affine Lie algebra
• Virasoro algebra

References

• Sam B. Treiman; Roman Jackiw; David J. Gross, Lectures on current algebra and its applications. Princeton Series in Physics. Princeton University Press, Princeton, N.J., 1972. x+362 pp.