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I found on this webpage:

http://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/costate.pdf

page 1, on the bottom

that

[tex] e^{\phi^* a } f(a^{\dagger} , a ) = f(a^{\dagger} + \phi^*, a) e^{\phi^* a }[/tex]

I have tried to prove this, writing both as taylor series, but the problem is to understand the "hint" :(

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# Exponential of creation/annihilation operators

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