advanced_notions:quantum_field_theory:anomalies

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advanced_notions:quantum_field_theory:anomalies [2019/01/31 11:49] jakobadmin |
advanced_notions:quantum_field_theory:anomalies [2019/07/01 09:37] (current) jakobadmin [Concrete] |
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+ | A classical theory possesses a symmetry if the action $S(\phi)$ is unchanged by a transformation $\phi \to \delta \phi$. In a quantum theory, however, we have a symmetry if the path integral $\int D \phi e^{iS(\phi)}$ is invariant under a given transformation $\phi \to \delta \phi$. The key observation is now that invariance of the action $S(\phi)$ does not necessarily imply invariance of the path integral since the measure $D \phi$ can be non-invariant too. In more technical terms, the reason for this is that whenever we change the integration variables, we need to remember that the Jacobian can be non-trivial. | ||

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An anomaly is an obstruction to the construction of a quantum theory that has the same symmetry group as its action. | An anomaly is an obstruction to the construction of a quantum theory that has the same symmetry group as its action. | ||

advanced_notions/quantum_field_theory/anomalies.txt · Last modified: 2019/07/01 09:37 by jakobadmin

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