Isomorphisms of $\text{Spin}\left(\frac{1}{2}\right)$ to $\text{SU}(1,1)-Boson$: Universal Enveloping and Kangni-type Transformation

In this study we investigate the nexus between the $\text{Spin}(\frac{1}{2})$ and the $\text{SU}(1,1)$-quasi boson Lie structure and reveal related properties as well as some decomposition of spin particles. We show that the $\text{SU}(1,1)$-quasi boson has a left invariant Haar measure and we ascertain its spherical Fourier transformation. We finally show that this spherical Fourier transformation of type delta is a Kangni-type transform when the Planck’s constant, $\mathrm{\hslash }=1$.