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Concept
Chiral anomaly
Summary
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have more left than right, or vice versa.
Such events are expected to be prohibited according to classical conservation laws, but it is known there must be ways they can be broken, because we have evidence of charge–parity non-conservation ("CP violation"). It is possible that other imbalances have been caused by breaking of a chiral law of this kind. Many physicists suspect that the fact that the observable universe contains more matter than antimatter is caused by a chiral anomaly. Research into chiral symmetry breaking laws is a major endeavor in particle physics research at this time.
The chiral anomaly originally referred to the anomalous decay rate of the neutral pion, as computed in the current algebra of the chiral model. These calculations suggested that the decay of the pion was suppressed, clearly contradicting experimental results. The nature of the anomalous calculations was first explained in 1969 by Adler and Bell & Jackiw. This is now termed the Adler–Bell–Jackiw anomaly of quantum electrodynamics. This is a symmetry of classical electrodynamics that is violated by quantum corrections.
The Adler–Bell–Jackiw anomaly arises in the following way. If one considers the classical (non-quantized) theory of electromagnetism coupled to fermions (electrically charged Dirac spinors solving the Dirac equation), one expects to have not just one but two conserved currents: the ordinary electrical current (the vector current), described by the Dirac field as well as an axial current When moving from the classical theory to the quantum theory, one may compute the quantum corrections to these currents; to first order, these are the one-loop Feynman diagrams. These are famously divergent, and require a regularization to be applied, to obtain the renormalized amplitudes.
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