Lüscher公式等价性证明

Equivalence Proof of Lüscher’s Formula

由于Lüscher's公式建立了连续空间中的散射相移和格点上能量之间的关系,使用时往往采用非相对论情形下的形式,而格点量子色动力学是基于量子场论也就是相对论性的理论。因此本文利用非相对论性量子力学和量子场论,证明了自旋为0和自旋为1/2的粒子在散射过程中Lüscher公式在非相对论情形下和相对论情形下是完全等价的。所得结果为研究强子-强子散射提供了理论基础,且在格点数值计算中具有非常重要的应用意义。

Lüscher's formula establishes the relationship between the scattering phase shift and the energy levels on lattice,and its non-relativistic form is usually chosen when it is being used.However,the lattice QCD is a relativistic theory based on the quantum field theory.Therefore,in this paper,the quantum mechanism and quantum field theory are used to prove that Lüscher's formulas in both non-relativistic and relativistic cases are fully equivalent in the scattering of spin-0 and spin-1/2 particles.The obtained results provide a theoretical basis for the study of the hadron-hadron scattering,and have found an important applications in lattice numerical calculations.