标准模型的一个可能的SLq（2）子结构
A Possible SLq(2) Substructure of the Standard Model
摘要：
我们研究了具有对称性$SU(3) \times SU(2) \times U(1)\times $全局$SLq(2)$的标准模型的量子群扩展。这个扩展模型的量子场位于$SLq(2)$代数的状态空间中。简正模或场量子携带因子$D^j_{mm^\prime} (q|abcd)$，它们是$SLq(2)$（也是纽结代数）的不可约表示。我们将这些场量子描述为量子结，并设置$(j,m,m^\prime)= 1/2 (N,w, \pm r+1)$，其中$(N,w,r)$分别被限制为经典结的（交叉，扭曲，旋转的数量）。在四个量子三叶和四个基本费米子族之间存在经验上的一一对应关系，这种对应关系可以表示为$(j,m,m^\prime)=3(t,-t_3, -t_0)$，其中四个量子三叶用$(j,m,m^\prime)$标记，而四个族在标准模型中用同位素和超荷指数$(t,t_3,-t_0)$标记。我们建议通过将$D_{-3t-3t_0}^{3t} (q| abcd) $附加到标准模型中由$(t,t_3, t_0)$标记的每个粒子的场算符，将这种相关性扩展到所有表示。那么基本费米子$(t=1/2)$属于$SLq(2)$的$j=3/2$表示。基本表象$j=1/2$的元素被称为前子，而$D_{-3t,-3t_o}^{3t}$可以被解释为描述由基本前子组成的复合粒子的创造算符。当表示为$D_{\frac w2 \frac{\pm r+1}2} ^{N/2}$时，$D_{m m^\prime}^j$也可以被解释为描述量子结。这些互补描述可以被理解为描述由具有$N$交叉的打结玻色子场结合的$N$前子的复合粒子。
英文摘要：
We examine a quantum group extension of the standard model with the symmetry $SU(3) \times SU(2) \times U(1)\times $ global $SLq(2)$. The quantum fields of this extended model lie in the state space of the $SLq(2)$ algebra. The normal modes or field quanta carry the factors $D^j_{mm^\prime} (q|abcd)$, which are irreducible representations of $SLq(2)$ (which is also the knot algebra). We describe these field quanta as quantum knots and set $(j,m,m^\prime)= 1/2 (N,w, \pm r+1)$ where the $(N,w,r)$ are restricted to be (the number of crossings, the writhe, the rotation) respectively, of a classical knot. There is an empirical one-to-one correspondence between the four quantum trefoils and the four families of elementary fermions, a correspondence that may be expressed as $(j,m,m^\prime)=3(t,-t_3, -t_0)$, where the four quantum trefoils are labelled by $(j,m,m^\prime)$ and where the four families are labelled in the standard model by the isotopic and hypercharge indices $(t,t_3,-t_0)$. We propose extending this correlation to all representations by attaching $D_{-3t-3t_0}^{3t} (q| abcd) $ to the field operator of every particle labelled by $(t,t_3, t_0)$ in the standard model. Then the elementary fermions $(t=1/2)$ belong to the $j=3/2$ representation of $SLq(2)$. The elements of the fundamental representation $j=1/2$ will be called preons and $D_{-3t,-3t_o}^{3t}$ may be interpreted as describing the creation operator of a composite particle composed of elementary preons. $D_{m m^\prime}^j$ also may be interpreted to describe a quantum knot when expressed as $D_{\frac w2 \frac{\pm r+1}2} ^{N/2}$ These complementary descriptions may be understood as describing a composite particle of $N$ preons bound by a knotted boson field with $N$ crossings.
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