%0 Journal Article
%T Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium £¿3 QFT
%A Dubravko Klabu£¿ar
%A Ivan Dadi£¿
%J -
%D 2019
%R https://doi.org/10.3390/particles2010008
%X 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 £¿ 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 ¦² F ( p 0 ) does not vanish when | p 0 | ¡ú ¡Þ and cannot be split to retarded and advanced parts. In the Glaser¨CEpstein approach, the causality is repaired in the composite object G F ( p 0 ) ¦² F ( p 0 ) . In the FTP approach, after repairing the vertices, the corresponding composite objects are G R ( p 0 ) ¦² R ( p 0 ) and ¦² A ( p 0 ) G A ( p 0 ) . In the limit d ¡ú 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 | £¿ | 0 £¿ = 0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit t ¡ú ¡Þ . View Full-Tex
%K out-of-equilibrium quantum field theory
%K dimensional renormalization
%K finite-time-path formalism
%U https://www.mdpi.com/2571-712X/2/1/8