Dadić, Ivan; Klabučar, Dubravko
(2019)
Causality and Renormalization in FiniteTimePath OutofEquilibrium ϕ3 QFT.
Particles, 2
(1).
pp. 92102.
ISSN 2571712X
Abstract
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 outofequilibrium QFT within the finitetimepath 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 selfenergy 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 Smatrix theory, the renormalized, finite part of Feynman selfenergy 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 ⟨0ϕ0⟩=0 of the Smatrix theory. The finite, oscillating energynonconserving tadpole contributions vanish in the limit t→∞ .
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