Algebraic Apect of Helicities in Hadron Physics

ORAL

Abstract

We examined the relation of polarization vectors and spinors of $ (1,0)\oplus(0,1)$ representation of Lorentz group in Clifford algebra $ Cl_{1,3}$, their relation with standard algebra, and properties of these spinors. $ Cl_{1,3}$ consists of different grades:e.g. the first and the second grades represent $ (1/2,1/2)$ and $ (1,0)\oplus(0,1)$ representation of spin groups respectively with 4 and 6 components. However, these Clifford numbers are not the helicity eigenstates and thus we transform them into combinations of helicity eigenstates by expressing them as spherical harmonics. We relate the spin-one polarization vectors and $(1,0)\oplus(0,1) $ spinors under one simple transformation with the spin operators. We also link our work with Winnberg's work [1] of a superfield of a spinors of Clifford algebra by giving a physical meaning to Grassmann variables and discuss how Grassman algebra is linked with Clifford algebra. \\[4pt] [1] J.O.Winnberg, J. of Math Phys Vol 18, 625 (1977).

Authors

  • Murat An

    North Carolina State University

  • Chueng Ji

    North Carolina State University