In theoretical physics, the Weyl transformation, named after German mathematician Hermann Weyl, is a local rescaling of the metric tensor:
which produces another metric in the same conformal class.
When quantum mechanical effects break the conformal invariance of a theory, it is said to exhibit a conformal anomaly or Weyl anomaly.
Weyl connections are a class of affine connections that is invariant, although no Weyl connection is individual invariant under Weyl transformations.
if, under the Weyl transformation, it transforms via Thus conformally weighted quantities belong to certain density bundles; see also conformal dimension.
Introduce a connection that depends also on an initial one-form
For the transformation We can derive the following formulas Note that the Weyl tensor is invariant under a Weyl rescaling.
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