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                \begin{document}$$\begin{aligned} {{\hat{\Psi }}}^{\pm }_{\mathbf{k}',s,\omega }\rightarrow {{\hat{\Psi }}}^{\pm }_{-\mathbf{k}',s,-\omega },\quad c\rightarrow c^{*}\;,\quad \phi \rightarrow -\phi \;, \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal}
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                \begin{document}$$c\in {\mathbb {C}}$$\end{document}$ is a generic constant appearing in $\documentclass[12pt]{minimal}
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                \begin{document}$$P(d\Psi )$$\end{document}$ or in $\documentclass[12pt]{minimal}
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                \begin{document}$$V(\psi )$$\end{document}$ and $\documentclass[12pt]{minimal}
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