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.
A global anomaly is the quantum violation of a global symmetry current conservation.
A global anomaly can also mean that a non-perturbative global anomaly cannot be captured by one loop or any loop perturbative Feynman diagram calculations—examples include the Witten anomaly and Wang–Wen–Witten anomaly.
The most prevalent global anomaly in physics is associated with the violation of scale invariance by quantum corrections, quantified in renormalization.
Since regulators generally introduce a distance scale, the classically scale-invariant theories are subject to renormalization group flow, i.e., 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 this scale anomaly.
Anomalies in abelian global symmetries pose no problems in a quantum field theory, and are often encountered (see the example of the chiral anomaly).
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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 physics, a gauge theory is a field theory in which the Lagrangian is invariant under local transformations according to certain smooth families of operations (Lie groups). The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators.
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").
The goal of this course is to explain the conceptual and mathematical bases of the Standard Model of fundamental interactions and to illustrate in detail its phenomenological consequences.
The course builds on the course QFT1 and QFT2 and develops in parallel to the course on Gauge Theories and the SM.
Some topics covered in this class are: The Index theorem, solitons, topological band insulators/superconductors, bulk-edge correpondence, quantum anomalies, quantum pumping, symmetry protected topolog
Explores B-physics anomalies, EFT analyses, and model-building considerations in the context of Lepton Flavor Universality violations and semi-leptonic decays of the b quark.