One of the earliest appearances of knots in physics occured in 1867 when Lord Kelvin put forward the idea that atoms were vortex tubes. More recently, knot theory is being studied as a possible means of quantizing gravity (Baez and Munian 1994). An early attempt to define the energy of a knot was done by Fukuhara (1988). This was based on the usual 1/r potential of electrostatics. Unfortunately, this potential doesn't give a finite energy when passing to a continuous charge distribution. It also isn't strong enough to prevent various parts of the knot from touching. More recently O'Hara (1991, 1992) has described a number of renormalized "energies" for knots. Freedman et al., have shown one of these energy func-tionals to be both scale and conformally invariant. They then used this to show that the least energy configuration over all knot types is the round circle.
展开▼
机译：在物理学中最早出现的结是在1867年，当时开尔文勋爵提出了原子是涡流管的思想。最近，正在研究结理论作为量化重力的一种可能方法（Baez and Munian 1994）。 Fukuhara（1988）进行了早期尝试来确定结的能量。这是基于通常的1 / r静电势。不幸的是，当传递到连续电荷分布时，这种势能不会提供有限的能量。它的强度也不足以阻止结的各个部分接触。最近，奥哈拉（O'Hara，1991，1992）描述了许多用于结的归一化“能量”。 Freedman等人已经显示出这些能量函数之一既是尺度的，又是保形不变的。然后，他们用它来表明，在所有结类型上，最少的能量配置是圆形。
展开▼
