In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a discrete symmetry that would otherwise be preserved in the classical theory. Theoretical physics attempts to understand the world by making a model of reality, used for rationalizing, explaining, and predicting physical phenomena through a physical theory. There are three types of theories in physics: mainstream theories, proposed theories and fringe theories. ... In physics, an anomaly is a classical symmetry — a symmetry of the Lagrangian — that is broken in quantum field theories. ...
Alternatively, the existence of a global anomaly implies that the measure of Feynman's functional integral cannot be defined globally. Richard Feynman Richard Phillips Feynman (May 11, 1918–February 15, 1988) (surname pronounced FINE-man) was one of the most influential American physicists of the 20th century, expanding greatly the theory of quantum electrodynamics. ... In physics, functional integration is integration over certain infinite-dimensional spaces. ...
The adjective "global" refers to the properties of a group that are not visible locally. For example, all features of a discrete group (as opposed to a Lie group) are global in character. The term group can refer to several concepts: Look up Group in Wiktionary, the free dictionary In music, a group is another term for band or other musical ensemble. ... In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ...
Many types of global anomalies must cancel for a theory to be consistent. An example is modular invariance, the requirement of anomaly cancellation for a part of a gravitational anomaly that deals with the large diffeomorphisms. Anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams In theoretical physics, a gravitational anomaly is an example of an anomaly: it is an effect of quantum mechanics - usually a one-loop diagram - that invalidates the general covariance of a theory of general relativity combined with some... In mathematics and theoretical physics, a large diffeomorphism is a diffeomorphism that cannot be continuously connected to the identity diffeomorphism (because it is topologically non-trivial). ...
Historically quantum anomalies have often been considered to be short-distance effects (ultraviolet effects, in the language of quantum field theory), as they arise during the process of renormalization, when some divergent integrals cannot be regularized in such a way that all the symmetries are preserved simultaneously.
In particular, the effects of anomalies are often felt at long distances, since the lack of this classical symmetry is often manifested in the physics of massless (or nearly massless) particles described by the theory.
Anomalies in abelian global symmetries pose no problems in a quantum field theory, and are often encountered (see the example of the chiral anomaly).
Martin Jacques: The death of Doha signals the demise of globalisation
This was the boom period of railroad construction and the advent of the ocean-going steamship.
And yet the diplomatic failures of that fateful summer led to the great slaughter of the trenches, the death of a substantial portion of the younger generation, and a virtual nervous breakdown of authority in politics and culture.
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