无自旋单粒子Yukawa模型的紫外性质
Ultraviolet Properties of the Spinless, One-Particle Yukawa Model
摘要：
我们考虑无自旋汤川模型的单粒子部分，它描述了核子与标量质量玻色子（中性介子）的实场的相互作用。核子和介子都有相对论色散关系。在这个模型中，我们研究了核子质量壳层对紫外截止$Λ$的依赖性。对于任意有限紫外截止，核子单粒子态都是在能量-动量空间的有界区域中构造的。我们确定了基态能量对$Λ$和耦合常数的依赖性。更重要的是，我们表明，这里考虑的模型变得基本上微不足道的限制$Λ\to\infty$，无论任何（核子）质量和自能重整化。我们的研究结果在小耦合制度。
英文摘要：
We consider the one-particle sector of the spinless Yukawa model, which describes the interaction of a nucleon with a real field of scalar massive bosons (neutral mesons). The nucleon as well as the mesons have relativistic dispersion relations. In this model we study the dependence of the nucleon mass shell on the ultraviolet cut-off $Λ$. For any finite ultraviolet cut-off the nucleon one-particle states are constructed in a bounded region of the energy-momentum space. We identify the dependence of the ground state energy on $Λ$ and the coupling constant. More importantly, we show that the model considered here becomes essentially trivial in the limit $Λ\to\infty$ regardless of any (nucleon) mass and self-energy renormalization. Our results hold in the small coupling regime.
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