Clifford algebra unitary group approach to many-electron correlation problem

Abstract

Unitary group approach (UGA) to the many-electron correlation problem is generalized by embedding the unitary group U(n) in a much larger group U(2n) via the rotation groups SO(m) with m=2n or 2n+1 and their covering group Spin (m). Exploiting the spinorial Clifford algebra basis associated with Spin (m), it is shown that an arbitrary N-electron configuration state can be represented as a linear combination of two-box Weyl tableaux of U(2n), and the explicit representation for U(n) generators as simple linear combinations of U(2n) generators is given. The problem of U(n) generator matrix element evaluation for two-column irreducible representations then reduces to an elementary problem of evaluation of generator matrix elements for the totally symmetric two-box representation of U(2n). Thus a general N-electron problem is effectively reduced to a number of two-boson problems. The proposed formalism also enables us to exploit other than Gelfand–Tsetlin coupling schemes and particle nonconserving operators.