We consider an analogue of the Lieb–Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb–Thirring constant converges to the optimal constant of the one-body Gagliardo–Nirenberg interpolation inequality without interaction.

中文翻译：

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强耦合极限下相互作用系统的Lieb-Thirring不等式

我们考虑具有均质排斥相互作用势但没有波函数反对称假设的量子系统的Lieb-Thirring不等式的类似物。我们证明，在强耦合极限中，Lieb-Thirring常数收敛到一单Gagalardo-Nirenberg插值不等式的最优常数，而没有相互作用。