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Particles 2019, 2(1), 92-102; https://doi.org/10.3390/particles2010008

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

1
Rudjer Bošković Institute, P.O. Box 180, 10002 Zagreb, Croatia
2
Physics Department, Faculty of Science-PMF, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia
*
Author to whom correspondence should be addressed.
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)
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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 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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