Hello! So I understand that in QFT and based on the second quantization, one introduce the hermitian operator ##\hat{\phi}(x)##. So, if we have a state with n particles ##|n>## we can get the configuration space representation as: ##\psi(x_1,..,x_n,t)=<0|\hat{\phi}(x_1)...\hat{\phi}(x_n)|n>## (please let me know if anything I said is wrong). Then I read that writing the action for a field, in the end we can derive ##H[\pi,\phi]##, with ##\pi## the conjugate momentum of ##\psi## and here is where I get confused. What is the meaning of ##\phi## without a hat? It means it is just a scalar field, not a field operator? So it is just as ##\phi## was previously, in the first quantization QM? And if in the end we go back to a scalar field and not an operator, what is the point of the second quantization? I.e., if we solve the Klein-Gordon equation for ##\phi(x)## we still get a plane wave, so where is the operator-like behavior of ##\phi##? And I see that both ##\phi## and ##\psi## appear in this formalism, so they can't represent both the same thing. Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Field operator

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