论文标题

经典重力状态的伯特 - 盐分方程

Bethe-Salpeter equation for classical gravitational bound states

论文作者

Adamo, Tim, Gonzo, Riccardo

论文摘要

伯特 - 盐分方程是对两体结合状态的非扰动,相对论和协变的描述。我们在结合重力系统中得出了两个巨大点颗粒(有或没有旋转)的经典伯特 - 盐分方程。这是一个递归关系,涉及经典幅度空间中的两个质子粒子图表,这是通过在内部重力交换上对对称化的识别来定义的。在这种情况下,我们观察到,领先的敌军近似与两体散射直接来自具有虚拟引力的连贯状态的单位性技术。更笼统地,我们通过在影响参数空间中指出经典内核来分析所有顺序求解经典的浆盐方程。我们阐明了这种经典的内核与汉密尔顿 - 雅各比的作用之间的联系,从而显现了经典结合和散射可观察到的分析延续。使用在动量空间中经典(无旋转和旋转)幅度的显式分析重新召集,我们进一步探索了具有结合态能量的极点和带有绑定状态波形的残基之间的关系。最后,我们讨论了Sommerfeld增强的相对论类似物,该类似物是针对约束状态横截面的。

The Bethe-Salpeter equation is a non-perturbative, relativistic and covariant description of two-body bound states. We derive the classical Bethe-Salpeter equation for two massive point particles (with or without spin) in a bound gravitational system. This is a recursion relation which involves two-massive-particle-irreducible diagrams in the space of classical amplitudes, defined by quotienting out by symmetrization over internal graviton exchanges. In this context, we observe that the leading eikonal approximation to two-body scattering arises directly from unitarity techniques with a coherent state of virtual gravitons. More generally, we solve the classical Bethe-Salpeter equation analytically at all orders by exponentiating the classical kernel in impact parameter space. We clarify the connection between this classical kernel and the Hamilton-Jacobi action, making manifest the analytic continuation between classical bound and scattering observables. Using explicit analytic resummations of classical (spinless and spinning) amplitudes in momentum space, we further explore the relation between poles with bound state energies and residues with bound state wavefunctions. Finally, we discuss a relativistic analogue of Sommerfeld enhancement which occurs for bound state cross sections.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源