Operator-Theoretical Research of Two-Body System in Non-Relativistic Quantum Field Theory

从算子理论的角度研究了非相对论量子场论中的二体系统。我们对所谓的双极化子形成时的问题特别感兴趣。现在让我们考虑三维晶体中两个电子与纵向光学声子耦合的情况。然后，一般来说，由于电子-声子相互作用，电子被包裹在声子云中。被包裹的电子就是所谓的极化子。如果两个电子之间的库仑斥力足够强，两个电子就会彼此相距很远，以至于每个电子都把自己打扮成一个单独的声子云。因此，两者之间没有声子交换。另一方面，如果两个电子之间的距离很短，一个共同的声子云抓住了两个电子，那么声子交换就发生了。在这种情况下，它们之间有可能产生吸引力，因此我们可以预期它们是相互绑定的。结合的两个极化子叫做双极化子。我们已经探讨了两个电子之间的拉锯战。我们已经阐明了双极化子问题的一些数学方面。

We have studied the two-body system in non-relativistic quantum field theory in the light of operator theory. In particular we have been interested in the problem when the so-called bipolaron forms.Let us consider two electrons coupled with longitudinal optical (LO) phonons in a 3-dimensional crystal now. Then, in general, an electron is dressed in a phonon cloud because of the electron-phonon interaction. The dressed electron is the so-called polaron. If the Coulomb repulsion between the two electrons is strong enough, the two electrons are so far away from each other that each electron dresses itself in an individual phonon cloud. Thus, there is no exchange of phonons between the two. On the other hand, if the distance between the two electrons is so short that a common phonon cloud grasps both electrons, then the phonon-exchange takes place. In this case, there is a possibility that attraction appears between them and thus we can expect that they are bound to each other. The bound two polarons is called a bipolaron. We have explored tug of war between the two electrons. We have clarified some mathematical aspects for the bipolaron problem.