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arXiv 2109.00549hep-phhep-th
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恢复微扰理论在高能下的失效

The Breakdown of Resummed Perturbation Theory at High Energies

Sebastian Schenk

摘要:

在弱耦合量子场论中,对涉及大量粒子产生的高能过程的计算,以前已经表明需要新的非微扰行为,甚至新的物理现象。在某些情况下,已经树级的计算可能会进入大秩序微扰理论的制度,因此需要仔细研究。我们表明,在标量量子场论与一个独特的全球最低,适当的图形化微扰膨胀预计捕捉所有相关的物理效应,微扰理论可能仍然遭受严重的缺陷,在高能量制度。作为一个例子,我们考虑计算的形式$1 \to n$在$φ^6$理论的正质量项的多粒子阈值振幅,并表明,他们可能会违反量子理论的大$n$的么正性,即使在所有领先的$n$量子修正的remation。我们进一步认为,这是一个通用的功能,高阶自相互作用的标量场理论超越$φ^4$,从而使后者独特的高能行为。

英文摘要:

Calculations of high-energy processes involving the production of a large number of particles in weakly-coupled quantum field theories have previously signaled the need for novel non-perturbative behavior or even new physical phenomena. In some scenarios, already tree-level computations may enter the regime of large-order perturbation theory and therefore require a careful investigation. We demonstrate that in scalar quantum field theories with a unique global minimum, where suitably resummed perturbative expansions are expected to capture all relevant physical effects, perturbation theory may still suffer from severe shortcomings in the high-energy regime. As an example, we consider the computation of multiparticle threshold amplitudes of the form $1 \to n$ in $φ^6$ theory with a positive mass term, and show that they may violate unitarity of the quantum theory for large $n$, even after the resummation of all leading-$n$ quantum corrections. We further argue that this is a generic feature of scalar field theories with higher-order self-interactions beyond $φ^4$, thereby rendering the latter unique with respect to its high-energy behavior.

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