Anomalies At Different Energy Scales
Quantum anomalies were discovered via the process of renormalization, when some divergent integrals cannot be regularized in such a way that all the symmetries are preserved simultaneously. This is related to the physics at the UV (i.e. at high energies). However, due to Gerard 't Hooft's anomaly matching condition, any chiral anomaly can be described either by the UV degrees of freedom (those relevant at high energies) or by the IR degrees of freedom (those relevant at low energies). Thus one cannot cancel the anomaly by some UV completion of the theory — an anomalous symmetry is simply not a symmetry of the theory, even though classically it looks as if it is.
Read more about this topic: Anomaly (physics)
Famous quotes containing the words energy and/or scales:
“The tendencies of the times favor the idea of self-government, and leave the individual, for all code, to the rewards and penalties of his own constitution, which work with more energy than we believe, whilst we depend on artificial restraints.”
—Ralph Waldo Emerson (1803–1882)
“It cannot but affect our philosophy favorably to be reminded of these shoals of migratory fishes, of salmon, shad, alewives, marsh-bankers, and others, which penetrate up the innumerable rivers of our coast in the spring, even to the interior lakes, their scales gleaming in the sun; and again, of the fry which in still greater numbers wend their way downward to the sea.”
—Henry David Thoreau (1817–1862)