 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 an 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. 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. ==global anomalies== a global anomaly is anomaly associated with global symmetry. ===scaling and renormalization=== the most prevalent global anomaly in physics is associated with the scaling symmetry, which results in renormalization. since regulators generally introduce a distance scale, the classically scale-invariant theories are subject to renormalization group flow, changing behavior with energy scale. for example, the large strength of the strong nuclear force results from a theory that is weakly coupled at short distances flowing to a strongly coupled theory at long distances, due to the scaling anomaly. ===rigid symmetries=== anomalies in abelian global symmetries pose no problems in a quantum field theory, and are often encountered (see the example of the chiral anomaly). in particular the corresponding symmetries can be fixed by fixing the boundary conditions of the path integral. ===large gauge transformations=== global anomalies in symmetries that approach the identity sufficiently quickly at infinity do, however, pose problems. in known examples such symmetries correspond to disconnected components of gauge symmetries. such symmetries and possible anomalies occur, for example, in theories with chiral fermions or self-dual differential forms coupled to gravity in 4k&nbsp;+&nbsp;2 dimensions, and also in the witten anomaly in an ordinary 4-dimensional su(2) gauge theory. as these symmetries vanish at infinity, they cannot be constrained by boundary conditions and so must be summed over in the path integral. the sum of the gauge orbit of a state is a sum of phases which form a subgroup of u(1). as there is an anomaly, not all of these phases are the same, therefore it is not the identity subgroup. the sum of the phases in every other subgroup of u(1) is equal to zero, and so all path integrals are equal to zero when there is such an anomaly and the theory does not exist. an exception may occur when the space of configurations is 
Anomalies_in_physics