$$ T\overline{T} $$ deformations and the width of fundamental particles
$$ T\overline{T} $$ deformations and the width of fundamental particles
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$$ Toverline{T} $$变形和基本粒子的宽度
DOI：
10.1007/jhep04(2022)136
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发表时间：
2022
影响因子：
5.4
通讯作者：
Cardy J
中科院分区：
文献类型：
--
作者：
Cardy J
我们对相对论和非相对论系统中所谓的型形变提供了一个简单的几何意义。在可积量子场论中，能量流和动量流的叉积所引起的形变可以通过一个“CDD因子”来修正热力学Bethe方程。反过来，CDD因子可以被解释为散射过程中产生的额外的固定位移：一个有限的宽度加到基本粒子上（或者，如果是负的，加到它们之间的自由空间上）。我们认为，这种物理效应是一种普遍的方式来理解变形，无论是在经典和量子系统。我们首先在具有粒子守恒和平移不变性的非相对论系统中，使用由粒子和动量的密度和电流形成的变形来证明这一点。这在运动方程的层次上是成立的，对于任何相互作用势，无论是可积的还是不可积的。然后，我们认为，并显示在自由相对论粒子系统中的类似技术，thatdeformations的相对论系统产生的等效现象，占长度收缩。我们还表明，在相对论和非相对论的情况下，粒子的宽度相当于一个状态依赖的变化的度量，其中的距离函数折扣粒子的宽度，或计数的额外的自由空间。这推广和解释了已知的依赖于场的坐标变化描述变形。结果连接这样的变形与广义流体力学，散射位移，粒子的宽度和状态依赖的变化度量之间的关系已经建立。
We provide a simple geometric meaning for deformations of so-calledtype in relativistic and non-relativistic systems. Deformations by the cross products of energy and momentum currents in integrable quantum field theories are known to modify the thermodynamic Bethe ansatz equations by a “CDD factor”. In turn, CDD factors may be interpreted as additional, fixed shifts incurred in scattering processes: a finite width added to the fundamental particles (or, if negative, to the free space between them). We suggest that this physical effect is a universal way of understandingdeformations, both in classical and quantum systems. We first show this in non-relativistic systems, with particle conservation and translation invariance, using the deformation formed out of the densities and currents of particles and momentum. This holds at the level of the equations of motion, and for any interaction potential, integrable or not. We then argue, and show by similar techniques in free relativistic particle systems, thatdeformations of relativistic systems produce the equivalent phenomenon, accounting for length contractions. We also show that, in both the relativistic and non-relativistic cases, the width of particles is equivalent to a state-dependent change of metric, where the distance function discounts the particles’ widths, or counts the additional free space. This generalises and explains the known field-dependent coordinate change describingdeformations. The results connect such deformations with generalised hydrodynamics, where the relations between scattering shifts, widths of particles and state-dependent changes of metric have been established.