Erasure code: Difference between revisions
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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, | |||
:<math>[\rho^a(\vec{x}),\rho^b(\vec{y})]=if^{ab}_c\delta(\vec{x}-\vec{y})\rho^c(\vec{x})</math> | |||
where f are the structure constants of the Lie algebra. If space is a one dimensional circle, there may exist [[Group extension#Central extension|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. | |||
[[Category:Quantum field theory]] | |||
[[Category:Lie algebras]] | |||
{{quantum-stub}} | |||
{{algebra-stub}} | |||
Revision as of 22:26, 12 August 2013
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}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d66035e5d2436b9f5a49b28ef70e7a3491353aa5)
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.