View source for Chiral anomaly

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One of the quantum-field theoretic manifestations of chiral dissymmetry or chiral asymmetry. Chiral anomaly in $2$-dimensional [[Quantum field theory|quantum field theory]] means that the quantum field observables from the left and the right sectors of a field model do not commute. Chiral anomaly is deeply related to non-commutative [[Geometry|geometry]] and the theory of anti-commutative algebras (cf. [[Anti-commutative algebra|Anti-commutative algebra]]), which are not Lie algebras [[#References|[a1]]], [[#References|[a2]]]. Namely, if the chiral sectors admit symmetries described by a semi-simple [[Lie algebra|Lie algebra]] $g$, then the whole model possesses symmetries, whose generators belong to the Borel–Lie anti-commutative central extension of the double $g+g$ (an anti-commutative algebra is called a Borel–Lie algebra (or BL-algebra) if every solvable subalgebra of it is a [[Lie algebra|Lie algebra]]).

Field models with chiral anomaly are efficiently used for anomalous stereo-synthesis (e.g., octonionic stereo-synthesis) in real-time interactive binocular video-systems.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  D. Juriev,   "Noncommutative geometry, chiral anomaly in the quantum projective $sl(2,C)$-invariant field theory and $jl(2,C)$-invariance"  ''J. Math. Phys.'' , '''33'''  (1992)  pp. 2819–2822</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  D. Juriev,   "Erratum"  ''J. Math. Phys.'' , '''34'''  (1993)  pp. 1615</TD></TR></table>