论文标题
有限时间路径的因果关系和重新归一化$ ϕ^3 $ qft
Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium $ϕ^3$ QFT
论文作者
论文摘要
我们的目的是为量子场理论（QFT）形式主义做出贡献，可用于描述短期现象，尤其是在重离子碰撞中占主导地位。我们在有限的时间路径形式主义（FTP）和重新归一化理论（RT）中制定了平衡QFT。 FTP和RT的潜在冲突通过使用绿色功能和维度重新归一化（DR）的智障/高级/高级（$ r/a $）基础，以$ g ϕ^3 $ qft进行了研究。例如，（及时）自动能源回路后立即进行顶点，因为积分差异不足。我们“维修”它们，同时保持$ d <4 $，以在这些顶点获得节能。在S-Matrix理论中，Feynman自我能源$σ_{f}（p_0）$的重新归一化的有限部分在$ | p_0 | \ rightarrow \ infty \ infty $时不会消失，并且不能拆分为智障和高级零件。在glaser-epstein方法中，在复合对象$ g_f（p_0）σ_{f}（p_0）$中修复了因果关系。在FTP方法中，修复顶点后，相应的复合对象为$ g_r（p_0）σ_{r}（p_0）$和$σ_{a}（p_0）g_a（p_0）$。在限制$ d \ rightarrow 4 $中，一个人获得了因果qft。 t的贡献分解为分歧和有限的部分。差异化条件$ \ langle 0 | ϕ | 0 \ rangle = 0 $ s-matrix理论消除了差异，恒定组件。有限的，振荡的能量促进的t贡献在限制$ t \ rightarrow \ infty $中消失。
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 $.
