Conformal anomaly
It is related to the renormalization group, or the "running of coupling constants," when they are viewed at different mass scales.In the sense of Weyl, mass (or length) are defined by the metric, and coordinates are simply scale-less book-keeping devices.There is an extensive literature involving spontaneous breaking of Weyl symmetry in four dimensions, leading to a dynamically generate Planck mass together with inflation.[1] [2] A conformal quantum theory is therefore one whose path integral, or partition function, is unchanged by rescaling the metric (together with other fields).As a result, the trace of the stress tensor must vanish for a conformally invariant theory.In quantum chromodynamics in the chiral limit, the classical theory has no mass scale so there is a conformal symmetry.Beside the anomaly (believed to contribute to about 20% of the proton mass[5][6]), the rest can be attributed to the light quarks sigma terms (i.e., the fact that quark have small non-zero masses that are not associated with the trace anomaly) believed to contribute to about 17%, and the quark and gluon energies believed to contribute to about 29% and 34% of the proton mass, respectively.Coleman and Weinberg showed how spontaneous symmetry breaking of electroweak interactions involving a fundamental Higgs scalar could occur via Feynmans loops.In fact, the Coleman-Weinberg mechanism can be traced entirely to the renormalization group running of the quartic Higgs coupling,[8] It has been conjectured that all mass in nature is generated by trace anomalies, hence by quantum mechanics alone.