费米弱相互作用的数学模型
A mathematical model for the Fermi weak interactions
摘要：
我们考虑一个数学模型的费米理论的弱相互作用图案根据著名的电流-电流耦合的量子电动力学。我们集中在μ子衰变成电子，正电子和中微子的例子，但其他例子被认为是以同样的方式。我们证明了描述这个模型的哈密顿量在一个足够小的耦合常数下在费米子Fock空间中有一个基态。此外，我们确定了绝对连续谱的哈密顿量和交换子估计，我们证明了该谱是绝对连续远离一个小邻域的阈值的自由哈密顿量。对于所有这些结果，我们没有使用任何红外截止或红外正则化，即使费米子与零质量的参与。
英文摘要：
We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons, positrons and neutrinos but other examples are considered in the same way. We prove that the Hamiltonian describing this model has a ground state in the fermionic Fock space for a sufficiently small coupling constant. Furthermore we determine the absolutely continuous spectrum of the Hamiltonian and by commutator estimates we prove that the spectrum is absolutely continuous away from a small neighborhood of the thresholds of the free Hamiltonian. For all these results we do not use any infrared cutoff or infrared regularization even if fermions with zero mass are involved.
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