arXiv 2212.080092022-12-15hep-thgr-qc

解析波函数

The Analytic Wavefunction

Santiago Agui Salcedo, Mang Hei Gordon Lee, Scott Melville, Enrico Pajer

备注：: 47+31 pages, 9 figures, 3 tables

摘要：

量子场论中的波函数是解决各种问题的宝贵工具，包括探测闵可夫斯基时空的内部和模拟德西特时空中的边界观测量。在这里，我们研究的波函数系数在闵可夫斯基作为其运动学的函数的解析结构。我们引入了一个离壳波函数截断的时间顺序的关联函数，并表明，它是解析的复能量平面上的负实轴上的可能的奇点除外。这些奇异性是由一个简单的能量守恒条件决定的。我们证实了这一点，通过发展一个朗道分析的波函数圈积分和证实我们的研究结果与几个明确的计算在标量场理论。这种分析结构使我们能够获得新的UV/IR总和规则的波函数，固定的系数在其低能量的扩展在相应的UV完成的不连续性的积分。与散射振幅的类似求和规则相反，波函数求和规则也可以约束全导数相互作用。我们明确验证这些新的关系在一个循环的顺序在简单的UV模型的轻和重标量。我们的结果，适用于洛伦兹不变和助推破缺理论，铺平了道路，推导波函数的正边界平坦和宇宙时空。

英文摘要：

The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski as a function of their kinematics. We introduce an off-shell wavefunction in terms of amputated time-ordered correlation functions and show that it is analytic in the complex energy plane except for possible singularities on the negative real axis. These singularities are determined to all loop orders by a simple energy-conservation condition. We confirm this picture by developing a Landau analysis of wavefunction loop integrals and corroborate our findings with several explicit calculations in scalar field theories. This analytic structure allows us to derive new UV/IR sum rules for the wavefunction that fix the coefficients in its low-energy expansion in terms of integrals of discontinuities in the corresponding UV-completion. In contrast to the analogous sum rules for scattering amplitudes, the wavefunction sum rules can also constrain total-derivative interactions. We explicitly verify these new relations at one-loop order in simple UV models of a light and a heavy scalar. Our results, which apply to both Lorentz invariant and boost-breaking theories, pave the way towards deriving wavefunction positivity bounds in flat and cosmological spacetimes.

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