Spinor Basis in Electron Correlation Studies

Spinor representations of generators of the Lie algebra of SO(N)(N=2n, 2n+1; n integer, have played a key role in a number of areas of Physics [1–5]. A general approach to these representations in a form suitable for practical applications has been of recent origin [6–8]. Starting with the unitary algebra of U(2n), the generators of SO(N) and U(n) were realised in the chain U(2n) ⊃ SO(2n+1) ⊃ SO(2n) ⊃ U(n). It was found that the symmetric bispinor basis spanning the representation [2 Ȯ] of U(2n) could be used to subduce the spin-free configurations spanning the representations [2N/2-s, 12s, Ȯ] of U(n). Some preliminary studies of generating the configuration space in this manner have recently been carried out for basis adapted for the chains U(n)⊃...⊃ U(1) [8] and U(n) ⊃ SO(n) ...⊃ SO(2) [9]. From a practical point of view this approach has a basic drawback. This is the fact that the simple one electron orbital description of spin-free configurations is masked in using the spinor basis. In the present study we examine the possibility of inducing a basis spanning the representations of U(2n) and SO(N) starting with the antisymmetric representations, [1N, Ȯ] (0≤N≤n; N integer) of U(n). The aim is to provide a simple interpretation of the spinor basis in terms of the tensor (integer) representations of U(n).