Nelson模型的部分经典极限
Partially classical limit of the Nelson model
摘要：
我们考虑Nelson模型，它描述了一个非相对论性的全同粒子通过Yukawa型相互作用耦合到一个可能无质量的标量玻色场的量子系统。我们研究了该模型的限制行为的情况下，玻色激发的数量变得无穷大，而耦合常数趋于零，在适当的意义。在这个极限下，适当重新标度的玻色场收敛到自由波或克莱因-戈登方程的经典解，这取决于场的质量是否为零，该解周围的量子涨落满足波或克莱因-戈登方程，非相对论性粒子的演化受量子动力学控制，外部势由先前的经典解给出。
英文摘要：
We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a situation where the number of Bose excitations becomes infinite while the coupling constant tends to zero in a suitable sense. In that limit the appropriately rescaled Bose field converges to a classical solution of the free wave or Klein-Gordon equation depending on whether the mass of the field is zero or not, the quantum fluctuations around that solution satisfy the wave or Klein-Gordon equation and the evolution of the nonrelativistic particles is governed by a quantum dynamics with an external potential given by the previous classical solution.
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