论文标题
具有压缩空间维度的理论中振幅的分散关系证明
Proof of dispersion relations for the amplitude in theories with a compactified space dimension
论文作者
论文摘要
在歧管$ \ mathbb {r}^{3,1} \ times s^1 $中，研究了非前方方向散射幅度的分析性能。从$ d = 5 $ Minkowski空间开始，质量$ m_0 $的标量字段理论开始。随后，一个空间维度被压缩到一个圆。所得理论的质谱是：（a）质量的巨大标量，$ m_0 $，与原始的五维理论相同，以及（b）庞大的kaluza-klein塔。我们得出了非前提分散关系，用于散射lehmann-symanzik-zimmermann对理论的激发kaluza-klein状态。为了完成此对象，首先，我们将Jost-Lehmann-Dyson定理推广为具有紧凑的空间维度的相对论场理论。接下来，我们展示了莱曼 - 马丁椭圆形的存在，部分波膨胀会收敛。事实证明，当$ | t | $位于Lehmann-Martin Ellipse中时，散射幅度满足固定的 - $ t $分散关系。
The analyticity properties of the scattering amplitude in the nonforward direction are investigated for a field theory in the manifold $\mathbb{R}^{3,1}\times S^1$. A scalar field theory of mass $m_0$ is considered in $D = 5$ Minkowski space to start with. Subsequently, one spatial dimension is compactified to a circle. The mass spectrum of the resulting theory is: (a) a massive scalar of mass, $m_0$, same as the original five dimensional theory and (b) a tower of massive Kaluza-Klein states. We derive nonforward dispersion relations for scattering of the excited Kaluza-Klein states in the Lehmann-Symanzik-Zimmermann formulation of the theory. In order to accomplish this object, first we generalize the Jost-Lehmann-Dyson theorem for a relativistic field theory with a compact spatial dimension. Next, we show the existence of the Lehmann-Martin ellipse inside which the partial wave expansion converges. It is proved that the scattering amplitude satisfies fixed-$t$ dispersion relations when $|t|$ lies within the Lehmann-Martin ellipse.
