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The theoretical symmetry of physical laws under the transformation of time reversal, that is t -> -t.

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How is the retarded Green's function modified under the action of time-reversal operator?

Suppose I have a time-reversal symmetric Hamiltonian, $$\hat{H} = \sum_{\vec p} \begin{pmatrix} c^\dagger_{\vec p,\uparrow} & c^\dagger_{\vec p,\downarrow} \end{pmatrix} \underbrace{\begin{pmatrix} \ …
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