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})](../I/m/6aaa46f28d7c10f2f6cd77a0ce83e141.png)
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.