薛定谔系统的大电荷展开
The large-charge expansion for Schrödinger systems
摘要：
在这篇笔记中，我们执行的大电荷展开的非相对论系统的整体$U(1)$对称性在$3+1$和$2+1$时空维度，由应用到酉费米气体和任意子的动机。这些系统不具有完全的共形不变性，但在薛定谔群下是不变的。同样在这里，低能物理是由戈德斯通玻色子编码的，这是由于在固定电荷时打破了全局对称性。我们发现，在$2+1$维和更高的，有一个大的电荷展开，其中量子校正被抑制相对于下到领先的阶项在拉格朗日。给出了基态能量和声速的次高阶表达式。
英文摘要：
In this note, we perform the large-charge expansion for non-relativistic systems with a global $U(1)$ symmetry in $3+1$ and $2+1$ space-time dimensions, motivated by applications to the unitary Fermi gas and anyons. These systems do not have full conformal invariance, but are invariant under the Schrödinger group. Also here, the low-energy physics is encoded by a Goldstone boson which is due to the breaking of the global symmetry when fixing the charge. We find that in $2+1$ dimensions and higher, there is a large-charge expansion in which quantum corrections are suppressed with respect to the next-to-leading order terms in the Lagrangian. We give the next-to-leading-order expressions for the ground state energy and the speed of sound.
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