论文标题
通过线性代数$ 2 $ - 启动器
$2$-Spinors via Linear Algebra
论文作者
论文摘要
我们提供了一个简化的帐户，其中包括$ 2 $ spinors，直至dirac方程，而不是线性代数的资源。我们证明，狄拉克捆绑包与关联的捆绑包$ \ mathrm {sl} _2（\ Mathbb {c}）\ Times _ {\ Mathrm {su} _2 _2} _2} s $和$ \ MATHRM {SL} _2（\ Mathbb {C \ Mathbb {C}）） \ times _ {\ mathrm {su} _2} \ bar {s} $。 DIRAC方程的解决方案确定了一对共轭$ 2 $ spinor字段，上面是大量壳$ x_m $。
We give a streamlined account of $2$-spinors, up to and including the Dirac equation, using little more than the resources of linear algebra. We prove that the Dirac bundle is isomorphic to the associated bundles $\mathrm{SL}_2(\mathbb{C}) \times_{\mathrm{SU}_2} S$ and $\mathrm{SL}_2(\mathbb{C}) \times_{\mathrm{SU}_2} \bar{S}$. A solution of the Dirac equation determines a pair of conjugate $2$-spinor fields over the mass shell $X_m$.
