文摘
We construct the d-dimensional “half” Schrxf6;dinger equation, which is a kind of the root of the Schrxf6;dinger equation, from the (d+1)-dimensional free Dirac equation. The solution of the “half” Schrxf6;dinger equation also satisfies the usual free Schrxf6;dinger equation. We also find that the explicit transformation laws of the Schrxf6;dinger and the half Schrxf6;dinger fields under the Schrxf6;dinger symmetry transformation are derived by starting from the Klein–Gordon equation and the Dirac equation in d+1 dimensions. We derive the 3- and 4-dimensional super-Schrxf6;dinger algebra from the superconformal algebra in 4 and 5 dimensions. The algebra is realized by introducing two complex scalar and one (complex) spinor fields and the explicit transformation properties have been found.