AI 中文总结
该研究定义了非整数幂律场论的量子提升方法，将其应用于σ=4的珀施尔-泰勒模型，发现阶数为介子质量或更大的β形变可抑制其激发概率的发散。
AI 中文摘要
具有非整数幂律α的势场的场论已在诸多领域得到应用，但通常被认为除了作为有效模型外，无法提升为量子场论。我们通过将经典势展开为厄米多项式，再在由参数β偏移的质量标度处进行正规序来定义量子提升。我们发现当α>2时，对于足够大的β，真空态可在通常的福克态中进行微扰展开。我们将此应用于σ=4的珀施尔-泰勒模型，该模型具有φ^(5/2)势。由于势的三阶导数在每个真空中发散，人们预期真空中的三点相互作用会发散。该模型的扭结具有三个形状模式，且最不束缚的模式延伸至真空深处，其被辐射激发的概率显然发散。我们表明，阶数为介子质量或更大的β形变足以抑制该发散，尽管如此，这仍会导致激发概率被逆耦合的β依赖分数次幂增强。
英文摘要
Field theories whose potentials have noninteger power laws $α$ have found many applications, but are often claimed to have no lift to quantum field theory except as effective models. We define quantum lifts by expanding the classical potential in Hermite polynomials and then normal ordering at a mass scale shifted by a parameter $β$. We find that when $α>2$, for sufficiently large $β$, the vacuum state can be perturbatively expanded in usual Fock states. We apply this to the following problem. The $σ=4$ Pöschl-Teller model has a $ϕ^{5/2}$ potential. As the third derivative of the potential diverges in each vacuum, one expects the three point interactions to diverge in the vacuum. The model's kink has three shape modes and the least bound mode extends so far into the vacuum that its probability of being excited by radiation apparently diverges. We show that a deformation $β$ of order the meson mass or larger is sufficient to tame this divergence, although it nonetheless results in an excitation probability which is enhanced by a $β$-dependent fractional power of the inverse coupling.
Comments18 pages, 1 figure
