论文标题
扭结状态的内部产品减少
A Reduced Inner Product for Kink States
论文作者
论文摘要
经典场理论中的孤子对应于量子场理论中的状态。如果空间尺寸是无限的,则动量本征态不可正常化。这会导致红外差异,通常通过波数据包或压缩正规化。但是,在某些应用中,两种可能性都是不可取的。在本说明中,我们在翻译不变的扭结状态上引入了有限的内部产品,该产品使我们能够计算涉及这些不可弥补状态的概率。从本质上讲,它是翻译组通常内部产品的商。我们为减少的内部产品提供了一个令人惊讶的简单公式,该公式不需要对状态的零模式依赖性的了解,但包括校正,该校正是说明零模式和正常模式之间的混合,并且随着扭结移动的移动。作为一个应用程序,我们表明对介子乘法的初始和最终状态校正消失了。但是,我们发现在初始状态下的跨胶结术语的极需要无限的假想转移。
Solitons in classical field theories correspond to states in quantum field theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads to infrared divergences, which are generally regularized via wave packets or by compactification. However, in some applications both possibilities are undesirable. In the present note, we introduce a finite inner product on translation-invariant kink states that allows us to compute probabilities involving these nonnormalizable states. Essentially, it is the quotient of the usual inner product by the translation group. We present a surprisingly simple formula for the reduced inner product, which requires no knowledge of the zero-mode dependence of the states but includes a correction which accounts for the mixing between zero modes and normal modes as the kink moves. As an application, we show that initial and final state corrections to meson multiplication vanish. However, we find that the pole of the subleading term in the initial state requires an infinitesimal imaginary shift.