Advanced Concepts in Quantum Field Theory by James M. Cline

Author:James M. Cline
Language: eng
Format: epub
ISBN: 9783030561680
Publisher: Springer International Publishing

(10.72)

However, under this symmetry, so that . A nonvanishing VEV for would therefore break the symmetry, in contradiction to the fact that the symmetry does exist in the underlying Lagrangian. You can see this explicitly by considering the path integral, and changing variables from to :

(10.73)

Both the action and the path integral measure are invariant under this phase transformation. For the action this was obvious; for the measure, we note that the determinant of the Jacobian matrix is unity:

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