Hello. I am doing some reading on QED and am getting a bit confused on the different conventions used. In Matthew Schwartz's book we have the Lagrangian given as:(adsbygoogle = window.adsbygoogle || []).push({});

L_{QED}= -¼ F_{μν}F^{μν}+ iψ^{*}γ^{μ}(∂_{μ}+ ieA_{μ})ψ - V(ψ^{*}ψ)

And the path integral factor is exp(iS).

In another text, however, I see the QED lagrangian given as:

L_{QED}= ¼ F_{μν}F^{μν}+ ψ^{*}γ^{μ}(∂_{μ}+ eA_{μ})ψ - V(ψ^{*}ψ)

And the exponential factor in the path integral is exp(-S).

How can I see that these two conventions are physically the same? In particular, what is the difference between using exp(iS) and exp(-S) in the path integral?

Thanks!

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# Path Integral Conventions

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