Consider $a$ be a bosonic operator, and we define $\Phi = a+a^{\dagger}$ and it is clear that $\Phi^{\dagger}=\Phi$ that implies "Majorana Boson". Now, i want to find the coherent states for this case in the following way \begin{equation} \Phi|\phi\rangle = \phi|\phi\rangle \end{equation} Now how do i proceed to find the eigen states and eigenvalues of $\Phi$. How to write a coherent state path integral for this? Any suggestions?
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