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[tex]\int d\phi e^{iS[\phi]}=\int d\phi' J e^{iS'[\phi']} [/tex]

where J is the Jacobian. If the transformation of variables to phi' is a symmetry of the action [i.e., S'=S], then this becomes:

[tex]\int d\phi e^{iS[\phi]}=\int d\phi' J e^{iS[\phi']} [/tex]

But doesn't this imply that the Jacobian has to equal one?

But surely that doesn't have to be true in general? If the action has a symmetry, and you perform the change of coordinates corresponding to the symmetry transformation, then does the Jacobian of that transformation have to equal one?

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# Jacobian in path integral equal to one?

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