For the Hamiltonian , H=hw (a*a). How could one evaluate the green's function in the path integral approach using coherent states for a fermion (or boson) ? In particular, one can evaluate this in phase space using (q, p) as integral variable and calculate the green's function in terms of the position variable. How do one determine the same in the coherent state path integral for the above harmonic oscillator (second quantized notation) ? Most importantly how could one evaluate the step by step integral for every time slice in coherent states to get the green's function ? Please suggest some reference where it has worked out
Dear Vigneshwaran Kannan, in addition to the interesting reference by Prof. Behnam Farid
, I think the thermal coherent state approach is directly related to the phase space. A single-mode thermal coherent state is produced by displacing a thermal mixed state in phase space, in addition, the coherent state by definition is an eigenstate of the annihilation operator in the Heisenberg picture which is adequate for the Green function formalism.https://en.wikipedia.org/wiki/Coherent_state
Oz-Vogt, J.; Mann, A.; and Revzen, M. "Thermal Coherent States and thermal Squeezed States". Journal of Modern Optics, 38 (12): 2339–2347, 1991.
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