AI 中文总结
该研究在色玻璃凝聚框架下构建快速运动强子的软胶子光锥波函数及演化算符至\(\mathcal{O}(g^{2})\)阶，通过玻恩 - 奥本海默分离等方法确定系数，应用中对角化软哈密顿量，发现福克扇区非对角混合元素抵消，背景场能量与\(\rho^{2}\)成正比。
AI 中文摘要
在色玻璃凝聚（CGC）框架下，我们在纯杨 - 米尔斯理论（\(N_f = 0\)）中构建了一个快速运动强子的软胶子光锥波函数以及相关的酉演化算符\(\Omega\)至\(\mathcal{O}(g^{2})\)阶。在光锥规范下，我们对快速价模和软模进行玻恩 - 奥本海默分离并实施程函近似，使\(\Omega\)能写成软胶子产生和湮灭算符的全正规序级数。展开系数是不对易价色荷密度算符\(\rho\)的泛函。我们通过光锥微扰理论（LCPT）中的幺正性和显式图计算来确定系数。作为应用，我们将纯杨 - 米尔斯软哈密顿量对角化至\(g\)和\(g^{2}\)阶，表明福克扇区之间的非对角混合元素抵消，导致相干背景场能量与\(\rho^{2}\)成正比。
英文摘要
We construct the soft gluon light cone wave function of a fast moving hadron and the associated unitary evolution operator $Ω$ up to $\mathcal{O}(g^{2})$ in pure Yang Mills theory $(N_{f} = 0)$, within the Color Glass Condensate (CGC) framework. Working in light cone gauge, we perform a Born Oppenheimer separation between fast valence and soft modes and implement the eikonal approximation, which allows $Ω$ to be written as a fully normal ordered series in soft gluon creation and annihilation operators. The expansion coefficients are functionals of the non-commuting valence color charge density operators $ρ$. We fix the coefficients by using the unitarity and explicit diagrammatic calculations within light-cone perturbation theory (LCPT). As an application, we diagonalize the pure Yang Mills soft Hamiltonian through orders $g$ and $g^{2}$ and show that the off diagonal mixing elements between Fock sectors cancel leading to the coherent background field energy proportional to $ρ^{2}$.
Commentsv2: 57 pages, 1 figure. Added references ; v1: 57 pages, 1 figure
