附加质量效应与希格斯机制
The Added Mass Effect and the Higgs Mechanism
摘要：
一个刚体在无粘性不可压缩流体中加速时，似乎会获得质量，这被编码为一个附加的质量张量。游泳者、气泡、潜水艇和飞艇因与其加速度成比例的相关“附加质量”力而减速，这与粘性阻力和浮力不同。在粒子物理学中，无质量的电子、夸克、$W$和$Z$玻色子在通过希格斯标量场时获得质量矩阵中编码的质量。在这篇简要的文章中，我们通过不同维度的势流的例子来介绍流体力学的附加质量效应，并利用与希格斯机制的对应关系[在Proc. R. Soc. A471：20140803（2015）]来将这与$W$和$Z$玻色子如何获得它们的质量，同时使光子没有质量联系起来。对应关系的希格斯标量场的流体，希格斯场的真空期望值的恒定流体密度和希格斯凝聚体周围的压缩波的流体中的量子波动。刚体的形状编码的模式，规范对称性突破相应的质量矩阵的特征值。刚体可能的加速度方向与规范李代数中的方向有关，其中规范李代数中的“平坦”方向对应于无质量光子。此外，物体的对称性与标量真空流形的对称性有关。希格斯玻色子可以被看作是围绕加速物体的长波长流体模式的模拟。
英文摘要：
A rigid body accelerated through an inviscid, incompressible fluid appears to gain mass, which is encoded in an added mass tensor. Swimmers, air bubbles, submarines and airships are slowed down by the associated `added mass' force proportional to their acceleration, which is distinct from viscous drag and buoyancy. In particle physics, otherwise massless electrons, quarks, $W$ and $Z$ bosons, moving through the Higgs scalar field acquire masses encoded in a mass matrix. In this expository article we give an introduction to the fluid mechanical added mass effect through examples of potential flows in various dimensions and exploit a correspondence with the Higgs mechanism [introduced in Proc. R. Soc. A471: 20140803 (2015)] to relate this to how the $W$ and $Z$ bosons can get their masses, while leaving the photon massless. The correspondence relates the Higgs scalar field to the fluid, the vacuum expectation value of the Higgs field to a constant fluid density and quantum fluctuations around the Higgs condensate to compressional waves in the fluid. The shape of the rigid body encodes the pattern of gauge symmetry breaking through the eigenvalues of the corresponding mass matrices. Possible directions of acceleration of the rigid body are related to directions in the gauge Lie algebra with a `flat' direction in the body corresponding to a massless photon. Moreover, symmetries of the body are related to those of the scalar vacuum manifold. The Higgs boson may be viewed as the analog of a long wavelength fluid mode around an accelerated body.
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