User Tools

Site Tools


advanced_notions:quantum_field_theory:anomalies

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
advanced_notions:quantum_field_theory:anomalies [2019/01/31 10:49]
jakobadmin
advanced_notions:quantum_field_theory:anomalies [2019/07/01 07:37] (current)
jakobadmin [Concrete]
Line 35: Line 35:
  
 <tabbox Concrete> ​ <tabbox Concrete> ​
 +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. ​
 +
 +----
 +
 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 07:37 by jakobadmin