Something seems a little weird to me: What are the dimensions of a generating functional, [itex]Z[j][/itex] -- say for real scalar field theory?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]Z[j]=\int\mathcal{D}\phi\,\exp\, i\!\int d^4x\left(\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+j\phi\right)[/tex]

Also, what about mass dimensions of the generating functional for connected Green's functions, [itex]W[j][/itex]? This is defined in terms of the log of the generating functional, [itex]Z[j][/itex].

[tex]Z[j]=e^{iW[j]}[/tex]

This seems a little pathological...

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# Dimensions and the Generating Functional

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