Physics question! Is it possible in a quantum field theory (e.g. Klein-Gordon, but also interactive QFTs) to compute the spectrum of the field operators or their conjugate momenta? Or only of other operators?
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Oh, vacuum expectation value. No, that's one number. I want the spectrum of the operator!
Ah, I see.. to be frank the answer is no .. it’s not as clean as QM :’(
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That was my thought. The reason I was thinking about this was because of Bohmian approaches (I know, I know, physicists tend to dislike such thoughts as heresy, but I'm a mathematician/philosopher), and without a nice L^2 space or at least good spectra, that gets tricky.
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I spent a bit of time (a very LITTLE bit of time) trying to figure out if there would be a way to calculate the spectra for the field operators. Could not think of one. Thought maybe it was my general lack of QFT and complex analysis.
End of conversation
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One thing we do in a confining theory is write down all the gauge invariant operators. This is how we get the meson and baryon spectrums We can also predict goldstone or pseudo goldstone bosons vía goldstones theorem
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