双费米子系统的相对论束缚态方程
Relativistic bound-state equations for two-fermion systems
摘要：
我们指出，用于双费米子系统QFT方程的自由单费米子传播子具有玻色子结构，在非相对论极限下，它转化为Klein-Gordon方程的单玻色子传播子，因而不满足费米子的Lehmann谱表示.本文从Lippmann-Schwinger积分方程出发，利用自由双费米子等时传播子满足Lehmann表象，得到了一个双费米子相对论波动方程。这个波动方程已被应用于电子-正电子系统。除了正电子素的本征态外，我们还找到了一个用束缚能$\simeq 2m$和束缚系统的极小质量描述深束缚态的解。
英文摘要：
We point out that the free single-fermion propagator which is used in the QFT equations for two-fermion systems, has a bosonic structure, transforms to the single-boson propagator for the Klein-Gordon equation in the nonrelativistic limit, and, therefore, does not satisfy the Lehmann spectral representation for fermions. Proceeding from the Lippmann-Schwinger integral equation, we obtain a two-fermion relativistic wave equation in which the free two-fermion equal-time propagator satisfying the Lehmann representation, is used. This wave equation has been applied to the electron-positron system. In addition to the eigenstates for positronium, we find a solution which describes a deep bound state with the binding energy $\simeq 2m$ and anomalously small mass of the bound system.
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