In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the classical theory. Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world 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 Let's say we have a Topological space M and a Topological group G and a principal G-bundle over M This leads to an inconsistency in the theory because the space of configurations which is being integrated over in the functional integral involves both a configuration and the same configuration after a large gauge transformation has acted upon it and the sum of all such contributions is zero and the space of configurations cannot be split into connected components for which the integral is nonzero.
Alternatively, the existence of a global anomaly implies that the measure of Feynman's functional integral cannot be defined globally. You may also be looking for Functional integration (neurobiology or Functional integration (sociology.
The adjective "global" refers to the properties of a group that are not visible locally. In Mathematics, a group is a set of elements together with an operation that combines any two of its elements to form a third element For example, all features of a discrete group (as opposed to a Lie group) are global in character. In Mathematics, a Lie group (ˈliː sounds like "Lee" is a group which is also a Differentiable manifold, with the property that the group
A famous example is an SU(2) Yang-Mills theory in 4D with an odd number of chiral fermions transforming as doublets under SU(2). Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations In Mathematics and Physics, in particular in the theory of the Orthogonal groups spinors are elements of a complex vector space introduced to expand the
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 over two dimensional worldsheets of genus 1 or more. In Theoretical physics, modular invariance is the invariance under the group such as SL(2Z of Large diffeomorphisms of the Torus. In Theoretical physics, a gravitational anomaly is an example of a Gauge anomaly: it is an effect of Quantum mechanics –usually a One-loop diagram In Mathematics and Theoretical physics, a large diffeomorphism is a Diffeomorphism that cannot be continuously connected to the identity diffeomorphism In String theory, the worldsheet is a two-dimensional Manifold which describes the embedding of the string in Spacetime. A genus (plural genera from Γένος Latin genus "descent family type gender" is a low-level Taxonomic
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