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Open AccessArticle

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

Rudjer Bošković Institute, P.O. Box 180, 10002 Zagreb, Croatia
Physics Department, Faculty of Science-PMF, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia
Author to whom correspondence should be addressed.
Particles 2019, 2(1), 92-102;
Received: 30 November 2018 / Revised: 6 January 2019 / Accepted: 9 January 2019 / Published: 18 January 2019
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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 g ϕ 3 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 Σ F ( p 0 ) does not vanish when | p 0 | and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object G F ( p 0 ) Σ F ( p 0 ) . In the FTP approach, after repairing the vertices, the corresponding composite objects are G R ( p 0 ) Σ R ( p 0 ) and Σ A ( p 0 ) G A ( p 0 ) . 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 . View Full-Text
Keywords: out-of-equilibrium quantum field theory; dimensional renormalization; finite-time-path formalism out-of-equilibrium quantum field theory; dimensional renormalization; finite-time-path formalism
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Dadić, I.; Klabučar, D. Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium ϕ3 QFT. Particles 2019, 2, 92-102.

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