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.
Received: 30 November 2018 / Revised: 6 January 2019 / Accepted: 9 January 2019 / Published: 18 January 2019
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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
QFT, by using the retarded/advanced (
) 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
, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy
does not vanish when
and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object
. In the FTP approach, after repairing the vertices, the corresponding composite objects are
. In the limit
, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition
of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit
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MDPI and ACS Style
Dadić, I.; Klabučar, D. Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium ϕ3 QFT. Particles 2019, 2, 92-102.
Dadić I, Klabučar D. Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium ϕ3 QFT. Particles. 2019; 2(1):92-102.
Dadić, Ivan; Klabučar, Dubravko. 2019. "Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium ϕ3 QFT." Particles 2, no. 1: 92-102.
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