多费米子接触理论
Multi-fermion systems with contact theories
摘要：
我们解决了量子束缚态存在的最低要求的问题。特别是，我们证明了零程动量无关的两体相互作用的少体系统是不稳定的衰变成集群，如果它的波函数的混合对称性是强制执行。我们认为，任何两体散射长度远大于其他尺度的理论都具有这种不稳定性。我们解释了这一点与领导级无π介子有效场论描述$A>4$核的稳定状态的能力。有限的相互作用范围被确定为一个充分条件的绑定混合对称系统。这个范围的最小值取决于系统接近么正性，成分的数量，以及三体光谱离散尺度不变性的具体实现。
英文摘要：
We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into clusters, if mixed-symmetry of its wave function is enforced. We claim that any theory in which the two-body scattering length is much larger than any other scale involved exhibits such instability. We exemplify this with the inability of the leading-order pionless effective field theory to describe stable states of $A>4$ nuclei. A finite interaction range is identified as a sufficient condition for a bound mixed-symmetry system. The minimal value of this range depends on the proximity of a system to unitarity, on the number of constituents, and on the particular realization of discrete scale invariance of the three-body spectrum.
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