Caldeira–Leggett dissipative bath: Ohmic spectral density J(ω) = η·ω; Legendre-transform path integral

Caldeira–Leggett model of quantum dissipation. Setup: a system coordinate q coupled linearly to an infinite bath of harmonic oscillators, with Ohmic spectral density J(ω) = η·ω up to cutoff ω_c. The bath is integrated out via path…