论文标题
狄拉克纺纱器的保形主要基础
Conformal Primary Basis for Dirac Spinors
论文作者
论文摘要
我们研究Minkowski Space中的Dirac方程的解决方案$ \ Mathbb {r}^{1，D+1} $，将其转换为Lorentz Group $ So（1，d+1）$下的$ D $ d $ - 二维的保形主要纺纱器。此类解决方案通过$ \ Mathbb {r}^d $和共形尺寸$δ$中的一个点进行参数化。属于主连续系列的一组波型，$δ= \ frac {d} 2 +iν$，分别在质量和无数案例中具有$ν\ geq 0 $和$ν\ in \ Mathbb {r} $，形成了Delta function formantial formanize dirac equintion的完整基础。在无质量的情况下，共形初级波函数与梅林转化的动量空间中的波形有关。
We study solutions to the Dirac equation in Minkowski space $\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primary spinors under the Lorentz group $SO(1,d+1)$. Such solutions are parameterized by a point in $\mathbb{R}^d$ and a conformal dimension $Δ$. The set of wavefunctions that belong to the principal continuous series, $Δ=\frac{d}2 + iν$, with $ν\geq 0$ and $ν\in \mathbb{R}$ in the massive and massless cases, respectively, form a complete basis of delta-function normalizable solutions of the Dirac equation. In the massless case, the conformal primary wavefunctions are related to the wavefunctions in momentum space by a Mellin transform.
