Clifford algebra unitary group approach to manyhyphen;electron correlation problem

摘要

Unitary group approach (UGA) to the manyhyphen;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) withm=2nor 2n+1 and their covering group Spin (m). Exploiting the spinorial Clifford algebra basis associated with Spin (m), it is shown that an arbitraryNhyphen;electron configuration state can be represented as a linear combination of twohyphen;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 twohyphen;column irreducible representations then reduces to an elementary problem of evaluation of generator matrix elements for the totally symmetric twohyphen;box representation of U(2n). Thus a generalNhyphen;electron problem is effectively reduced to a number of twohyphen;boson problems. The proposed formalism also enables us to exploit other than Gelfandndash;Tsetlin coupling schemes and particle nonconserving operators.