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This is a profound question at the heart of science. Indeed no little effort has been devoted to trying to understand whether the mathematics of quantum mechanics are simply a contrivance or reflect reality. Surprisingly, Bell discovered an experimental method to answer the question and the result is that quantum weirdness is an intrinsic aspect of nature. ...


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@Andrew's answer provides the big picture, but I'd like to give a few more specific pointers that hopefully may help. Questions 1-2: Does everything look correct so far? How to express these operators in terms of one-particle operators? So you want to set up single-particle analogues of the ladder operators using eigenstates of the 1st quantized ...


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Your question amounts to "explain slowly the first month of a quantum field theory course," so I am not going to be able to address everything you've brought up in your question. But, I will try to discuss some of the key points. For a free theory there is an equivalence (at least at physicist level of rigor) between the quantum field picture and the Fock ...



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