论文标题
标准型号和4组
Standard Model and 4-groups
论文作者
论文摘要
我们表明，基于N = 3的n = 3时，基于N-串联模块的对称对称性的分类概括变得自然而简单，并且相应的3型和4型仪表场必须分别为Dirac Spinor和Lorentz标量。因此，通过使用庞加莱4组，我们自然地将费米子和标量物质纳入相应的4个连接中。可以通过基于$ sl（2，\ mathbb {c}）\ times k $组的3加划入的模块将内部对称性包含在4组结构中，因此，对于$ k = u（1）\ times \ times su（2）\ times su（2）\ times su（3）$，我们可以将标准模型包含在此分类方案中。
We show that a categorical generalization of the the Poincaré symmetry which is based on the n-crossed modules becomes natural and simple when n=3 and that the corresponding 3-form and 4-form gauge fields have to be a Dirac spinor and a Lorentz scalar, respectively. Hence by using a Poincaré 4-group we naturally incorporate fermionic and scalar matter into the corresponding 4-connection. The internal symmetries can be included into the 4-group structure by using a 3-crossed module based on the $SL(2,\mathbb{C}) \times K$ group, so that for $K=U(1)\times SU(2) \times SU(3)$ we can include the Standard Model into this categorification scheme.
