论文标题

2D中的量子完美流体

The Quantum Perfect Fluid in 2D

论文作者

Dersy, Aurélien, Khmelnitsky, Andrei, Rattazzi, Riccardo

论文摘要

我们考虑定义完美不可压缩2D流体的场理论。该系统的一个独特特性是,围绕基态波动的二次作用既不具有质量或梯度项。从机械上讲,这构成了技术难题,因为它暗示着波动的希尔伯特空间不是一个空间,并且扰动理论是没有用的。如我们所示,适当的处理必须使用配置空间是保留Lie Group $ S \ Mathrm {diff} $的区域。 Lie组上的量子力学基本上是一个群体理论问题,但在我们的情况下是一个更难的问题,因为$ s \ mathrm {diff} $是无限的维度。但是,专注于2-torus $ t^2 $上的流体,我们可以利用众所周知的结果$ s \ mathrm {diff}(t^2)(t^2)\ sim su su(n)$ for $ n \ fo \ infty $,将有限$ n $减少到可拖动的情况下。 $ su(n)$提供了紫外线调节,但是可以在连续限制$ n \ to \ infty $的情况下定义物理数量。我们研究的主要结果是存在未包含的局部激发,Vortons,满足分散$ω\ propto k^2 $并带有涡旋偶极子。 Vortons还以非常独特的衍生相互作用为特征,其结构是由对称性固定的。从原始的不可压缩的流体偏离了原始的液体,我们构建了一类田间理论,从一开始就出现了Vortons,作为玻色粒或费米金本地领域的量子。

We consider the field theory that defines a perfect incompressible 2D fluid. One distinctive property of this system is that the quadratic action for fluctuations around the ground state features neither mass nor gradient term. Quantum mechanically this poses a technical puzzle, as it implies the Hilbert space of fluctuations is not a Fock space and perturbation theory is useless. As we show, the proper treatment must instead use that the configuration space is the area preserving Lie group $S\mathrm{Diff}$. Quantum mechanics on Lie groups is basically a group theory problem, but a harder one in our case, since $S\mathrm{Diff}$ is infinite dimensional. Focusing on a fluid on the 2-torus $T^2$, we could however exploit the well known result $S\mathrm{Diff}(T^2)\sim SU(N)$ for $N\to \infty$, reducing for finite $N$ to a tractable case. $SU(N)$ offers a UV-regulation, but physical quantities can be robustly defined in the continuum limit $N\to\infty$. The main result of our study is the existence of ungapped localized excitations, the vortons, satisfying a dispersion $ω\propto k^2$ and carrying a vorticity dipole. The vortons are also characterized by very distinctive derivative interactions whose structure is fixed by symmetry. Departing from the original incompressible fluid, we constructed a class of field theories where the vortons appear, right from the start, as the quanta of either bosonic or fermionic local fields.

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