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Could anyone tell if there exists an identity [tex]a_k^\dagger = a_{-k}[/tex] because intuitively there should be no difference between creating a particle with momentum k and destroying a particle with momentum -k.

If true is it possible to show that from the definition [tex]a_k = \frac{1}{√V}∫e^{ikx} a(x)[/tex]?

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# Creation operator in k-space

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