A Relation between the density matrix and the annihilation operator

richard_andy
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how to derive the output density operators
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This question is related to equation (1),(3), and (4) in the [paper][1] [1]: https://arxiv.org/abs/2002.12252
 
We often see discussions about what QM and QFT mean, but hardly anything on just how fundamental they are to much of physics. To rectify that, see the following; https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/66a6a6005101a2ffa86cdd48/original/a-derivation-of-maxwell-s-equations-from-first-principles.pdf 'Somewhat magically, if one then applies local gauge invariance to the Dirac Lagrangian, a field appears, and from this field it is possible to derive Maxwell’s...

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