In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory.
In classical physics, a classical anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking parameter goes to zero. Perhaps the first known anomaly was the dissipative anomaly in turbulence: time-reversibility remains broken (and energy dissipation rate finite) at the limit of vanishing viscosity.
In quantum theory, the first anomaly discovered was the Adler–Bell–Jackiw anomaly, wherein the axial vector current is conserved as a classical symmetry of electrodynamics, but is broken by the quantized theory. The relationship of this anomaly to the Atiyah–Singer index theorem was one of the celebrated achievements of the theory. Technically, an anomalous symmetry in a quantum theory is a symmetry of the action, but not of the measure, and so not of the partition function as a whole.
I like the spectral-flow viewpoint on chiral anomalies, as described for instance in Peskin & Schroeder, last part of Ch. 19.1 This appears to depend crucially on the concept of fermi sea level, making it specific to fermions. However, bosonic self-dual tensor fields also have an anomaly...
4/23/2016 = 5:37:05
How do you explain this? Instrument Failure? Pole Reversal?
I have a real doosy that has got me stumped.
I need to solve the following equation for v:
tan(v + ω) = tan(θ + Ω)sec(i)
The symbols stand for the following values in an elliptical orbit of one point source around another (on the celestial sphere):
where v = true anomaly; ω = argument of...
I've been wondering what is up with hydrogen. It shares little more than basic commonality with any other atom, this strikes me as strange as all atoms share some properties with those around them on the periodic table whether be it nuclear, physical, or chemical. I asked a reputable source and...