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All the part regarding the complex valued exponential is utterly nonsense. I ask for the author to make it more readable, and to explain the reason for this nonsense. In all books about QFT I've read I never found a paragraph so arrogant, incomprensible and at the same time without any justification. Before correcting, ask yourself what's the connection between the partition function and the scattering amplitudes! 94.161.151.2 (talk) 17:58, 18 February 2010 (UTC)
But while they can be interpreted as operators acting on a Hilbert space, they're just the normal fields in path integral formalism. The probability amplitudes are different - they're gotten as in the example given for the propagator. 24.82.134.18 (talk) 09:30, 18 June 2010 (UTC)