AI 中文总结
该研究针对量子场论中有限转动的因果性约束给相互作用玻色气体转动惯量计算带来的技术难题，在零角速度极限下定义转动惯量并采用常规量子场论技术，在$\phi^4$理论中验证了含环图重求和的相互作用效应与经典预期一致，转动惯量密度仍与焓密度成正比。
AI 中文摘要
多体量子系统对转动的响应可以用转动惯量来表征。对于经典气体，转动惯量可以表示为焓密度乘以到转动轴的径向距离平方的积分。在量子场论中，巨正则系综中的有限转动要求满足因果性约束。这一约束在处理用贝塞尔函数零点离散化的横向动量时带来了技术挑战。然而，我们在角速度为零的极限下定义转动惯量，此时因果性约束不再相关，并且可以应用常规的量子场论技术。我们在$\phi^4$理论中计算了转动惯量，并且令人惊讶地发现，包括环图重求和在内的相互作用效应与经典预期一致，且转动惯量密度仍然与焓密度成正比。
英文摘要
The response of many-body quantum systems to rotation can be characterized by the moment of inertia. For a classical gas, the moment of inertia can be expressed as the integral of the enthalpy density multiplied by the squared radial distance from the rotation axis. In quantum field theory, the finite rotation in the grand canonical ensemble demands the causality bound. This constraint imposes technical challenges in treating transverse momenta discretized with the Bessel function zeros. However, we define the moment of inertia in the limit of zero angular velocity, in which the causality constraint is irrelevant and ordinary quantum field theoretical techniques can be applied. We evaluate the moment of inertia in the $ϕ^4$ theory and find that, surprisingly, the interacting effects including the ring-diagram resummation are consistent with the classical expectation and the moment of inertia density remains proportional to the enthalpy density.
Comments16 pages, 1 figure
