论文标题
仪表理论中的几何限制
Geometric confinement in gauge theories
论文作者
论文摘要
1978年，弗里德伯格（Friedberg）和李（Lee）引入了Hadron的现象学孤子袋模型，概括了1974年在QCD制定后不久开发的MIT袋模型。在此模型中，由于与真实的标量场$ρ$耦合，夸克和胶子被限制在某个紧凑的区域$ s \ subset {\ mathbb r}^3 $之外，从运动方程式通过运动方程式确定。 Soliton Bag型号中的量规耦合正在作为半经典级别的$ρ$的逆力运行。我们表明，由于引入扭曲的产品指标$ {\ mathrm {d}} s^2_m +ρ^2 {\ mathrm {d}} s^2_g $上的翘曲产品指标$ {\ mathrm {d}} s^2_m +ρ^2_g $在主要$ g $ - bundle $ p（m，g）$ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ m = {\ mathbb r}^{3,1} $。在紧凑型域中限制夸克和胶子$ s \ subset {\ mathbb r}^3 $是捆绑包歧管$ m \ times $ m \ times g $ to $ m $ s $ s $ s $ s $的结果，这是由于集团歧管$ g $缩小了$ s $。我们将此类区域$ s $的形成描述为由订单参数字段$ρ$控制的动态过程。
In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real scalar field $ρ$ which tends to zero outside some compact region $S\subset{\mathbb R}^3$ determined dynamically from the equations of motion. The gauge coupling in the soliton bag model is running as the inverse power of $ρ$ already at the semiclassical level. We show that this model arises naturally as a consequence of introducing the warped product metric ${\mathrm{d}}s^2_M + ρ^2{\mathrm{d}}s^2_G$ on the principal $G$-bundle $P(M,G)\cong M\times G$ with a non-Abelian group $G$ over Minkowski space $M={\mathbb R}^{3,1}$. Confinement of quarks and gluons in a compact domain $S\subset{\mathbb R}^3$ is a consequence of the collapse of the bundle manifold $M\times G$ to $M$ outside $S$ due to shrinking of the group manifold $G$ to a point. We describe the formation of such regions $S$ as a dynamical process controlled by the order parameter field $ρ$.
