Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium $ϕ^3$ QFT
Ivan Dadić, Dubravko Klabučar
备注：
MDPI latex definitions, 11 pages, 2 figures, gives correctly Eq. (10) which was written erroneously in the version published in Particles 2019, 2, 92-102, but without affecting the rest of the paper
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 $|p_0|\rightarrow\infty$ 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 $d\rightarrow 4$, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition $\langle 0|ϕ|0\rangle =0$ of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit $t\rightarrow \infty $.
In this note we discuss the relation between the constraints imposed by causality in the bulk of $AdS$ and the condition of positivity of the energy measured in ideal calorimeters in a collider experiment in the dual CFT. We first extend the analysis in the literature and recover all bounds imposed by causality of the boundary theory in the bulk dynamics for all polarizations of the graviton and the gauge boson field. These results translate to specific bounds for the ratio of central charges $\frac{a}{c}$ in the dual CFT, already found by analyzing the energy one point function. Then, we gene…
We study the causality violation in the non-local quantum field theory (as formulated by Kleppe and Woodard) containing a finite mass scale $Λ$. We use $ϕ^{4}$ theory as a simple model for study. Starting from the Bogoliubov-Shirkov criterion for causality, we construct and study combinations of S-matrix elements that signal violation of causality in the one loop approximation. We find that the causality violation in the exclusive process $ϕ+ϕ\to ϕ+ϕ$ grows with energy, but the growth with energy, (for low to moderate energies) is suppressed to all orders compared to what one would expect pure…
We analyze the constraints that causality imposes on some of the particle detector models employed in quantum field theory in general, and in particular on those used in quantum optics (or superconducting circuits) to model atoms interacting with light. Namely, we show that disallowing faster-than-light communication can impose severe constraints on the applicability of particle detector models in three different common scenarios: 1) when the detectors are spatially smeared, 2) when a UV cutoff is introduced in the theory and 3) under one of the most typical approximations made in quantum opti…
The basics of RG equations for generic partition functions are briefly reviewed, keeping in mind an application to the Polyakov-de Boer-Verlindes description of the holomorphic RG flow.
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Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to $ϕ^3$ models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $θ$-deformed space and derive noncommutative gauge field actions.
On the link between finite QFT and standard RG approaches
Institute for Nuclear Research of the Russian Academy of Sciences（俄罗斯科学院核物理研究所）；Institute for Theoretical and Mathematical Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学理论与数学物理研究所）；Department of Particle Physics and Cosmology, Physics Faculty, M.V. Lomonosov Moscow State University（莫斯科国立大学物理学院粒子物理与宇宙学系）；Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（杜布纳联合核研究所鲍戈留博夫理论物理实验室）
Causality and realizability of local operations in quantum field theory
Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；University of Vienna, Faculty of Physics, Vienna Doctoral School in Physics, and Vienna Center for Quantum Science and Technology (VCQ)（维也纳大学物理学院维也纳物理学博士项目与维也纳量子科学与技术中心）
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Massachusetts Institute of Technology（麻省理工学院）；NSF AI Institute for Artificial Intelligence and Fundamental Interactions（美国国家科学基金会人工智能与基础相互作用研究所）；Université Paris Saclay（巴黎萨克雷大学）；CEA（法国原子能和替代能源委员会）；LIST（法国原子能和替代能源委员会实验室集成系统与技术研究所）；Université d’Abomey-Calavi（阿波美-卡拉维大学）
In a recent work arXiv:2008.08601, Halverson, Maiti and Stoner proposed a description of neural networks in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory, while finite $N$ corrections are taken into account by interactions (non-Gaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and power-counting in this context. Indeed, these usual space-time notions may not hold for neural networks (since inputs can be arbitrary), however, the renormalization …
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Perimeter Institute for Theoretical Physics（Perimeter理论物理研究所）；Department of Physics and Astronomy, McMaster University（麦克马斯特大学物理与天文系）；Center of Gravity, Niels Bohr Institute（尼尔斯·玻尔研究所引力中心）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文系）
A large class of Thermodynamic Bethe Ansatz equations governing the Renormalization Group evolution of the Casimir energy of the vacuum on the cylinder for an integrable two-dimensional field theory, can often be encoded on a tensor product of two graphs. We demonstrate here that in this case the two graphs can only be of $ADE$ type. We also give strong numerical evidence for a new large set of Dilogarithm sum Rules connected to $ADE\times ADE$ and a simple formula for the ultraviolet perturbing operator conformal dimensions only in terms of rank and Coxeter numbers of $ADE\times ADE$. We conc…
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Centro Atómico Bariloche（巴里洛切原子中心）；CONICET（阿根廷国家科学研究委员会）；Instituto Balseiro（巴尔塞罗研究所）；UNCuyo（门多萨大学）；CNEA（阿根廷核能委员会）；Instituto de Física de La Plata - CONICET（拉普拉塔物理研究所-阿根廷国家科学研究委员会）
We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world-line but that give a non null contribution on its world-line. The electron self-field energy tensor is integrable without the use of any kind of renormalization; there is no causality violation and no conflict with energy conservation in the electron equat…
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