We review and further develop the Keldysh functional integral technique for study of Lindbladian evolution many-body driven-dissipative quantum systems. A systematic pedagogical account dynamics generic bosonic fermionic Lindbladians is presented. Our particular emphasis on unique properties stationary distribution function, determined by Lyapunov equation. This framework applied to examples in...

The connection between many-body theory (MBPT)—in perturbative and nonperturbative form—and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-bod...

Critical exponents of a Bose system are calculated microscopically without an expansion in 1/n ore. As expected, quantum corrections are found to be absent and the results to agree with the 1/n expansion result, for n = 2, to 0(1/n). The purpose of this letter is to discuss the critical behavior of a quantum system, which exhibits a phase transition , without the commonly employed techniques of...