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            <title xml:lang="en">Limitations of Second Quantization Notation for Description of Superconductivity</title>
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              <p>A supercurrent in metals, once excited, can persist for many months and longer. If superconducting (SC) electrons are exchangeable with normal electrons, then the SC-electrons become normal (dissipative) for a while, whereas the newly created SC-electrons did not experience any electromotive force. So the total momentum (or angular momentum) of the SC-electrons and the supercurrent inevitably vanish. Hence, the SC-electrons don't hop into normal states, i.e. the SC-electrons occupy the SC-states permanently. If so, then the SC-electrons and normal electrons are distinguishable and non-exchangeable. This consideration should be taken into account by using the second quantization notation for description of SC-states, since in the second quantization approach all particles are assumed to be indistinguishable. The presence of local states in crystals also provides difficulties for applications of the second quantization approach. A possible approximation avoiding the difficulties is the 2-particle method and further iterations counting the whole band of paired states.</p>
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