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Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium ϕ3 QFT

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in gϕ3 QFT, by using the retarded/advanced ( R/A ) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We “repair” them, while keeping d<4 , to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy ΣF(p0) does not vanish when |p0|→∞ and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object GF(p0)ΣF(p0) . In the FTP approach, after repairing the vertices, the corresponding composite objects are GR(p0)ΣR(p0) and ΣA(p0)GA(p0) . In the limit d→4 , one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition ⟨0|ϕ|0⟩=0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit t→∞ .

out-of-equilibrium quantum field theory ; dimensional renormalization ; finite-time-path formalism

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