# Current algebra

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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,

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

- 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.