A one-loop Schwinger-Keldysh Wilsonian RG calculation generates a dissipative cross-coupling between time branches and predicts two reduced-space fixed points in d=4, related to the Gaussian and Wilson-Fisher fixed points.
In terms of the path integral, the effective action is then given by eiSeff [ϕ<] ≡ eiS0[ϕ<] Z Dϕ>eiS0[ϕ>]eiSint[ϕ<,ϕ>]
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Wilsonian renormalisation group and thermal field theory in the Schwinger-Keldysh closed-time-path formalism
A one-loop Schwinger-Keldysh Wilsonian RG calculation generates a dissipative cross-coupling between time branches and predicts two reduced-space fixed points in d=4, related to the Gaussian and Wilson-Fisher fixed points.