Dynamical variables in the Bethe-Salpeter formalism
Dynamical variables in the Bethe-Salpeter formalism
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DOI：
10.1098/rspa.1955.0261
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发表时间：
1955-12
期刊：
影响因子：
--
通讯作者：
S. Mandelstam
中科院分区：
文献类型：
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作者：
S. Mandelstam
结果表明，知道传播子在奇点附近的行为，不仅可以确定束缚态的质量，而且还可以确定两个束束态之间任何动力学变量的矩阵元。因此，通过在相应的Bethe-Salpeter波函数上积分某些表达式，能够找到耦合常数中的任意阶矩阵元。因此，可以找到这些波函数的归一化和正交化性质，这反过来又导致必须对它们的奇点施加在原点上的条件。因此，更多地阐明了戈尔茨坦关于束缚态连续无穷大的存在的困难。将这种形式推广到某些粒子可以是复合粒子的散射态，得到了S矩阵的表达式
It is shown that a knowledge of the behaviour of the propagators around their singularities enables one to determine not only the masses of bound states, but also the matrix element of any dynamical variable between two bound states. One is thus enabled to find such a matrix element, to any order in the coupling constant, by the integration of certain expressions over the corresponding Bethe-Salpeter wave-functions. As a consequence, it is possible to find normalization and orthogonality properties of these wave-functions, which in turn lead to the condition which must be imposed on their singularities a t the origin. More light is thus shed on Goldstein’s difficulty concerning the existence of a continuous infinity of bound states. The formalism is extended to scattering states in which some of the particles may be composite—in particular, an expression for the S-matrix is obtained