Coulomb gauge restriction

The wave function I q is the solution of the Hamilton operator or Fock operator of the molecular system without external perturbations, and it is related to the ground state energy Eo- The shielding operator within the Coulomb gauge restriction yields in the general form introduced by Ramsey in 1950 ... 

From the present perspective, an obvious weakness of these calculations is the restriction to the one-photon subspace of Fock space. Because every gauge (choice of g(x,x )) leads to its own commutation relations (42), each has its own Fock space so projection on a one-photon subspace is not gauge-invariant. We have previously shown [21] that the one-photon part ofHmt (i.e linear in the charge e) in an arbitrary gauge is related to the Coulomb gauge interaction (g1 = 0) by... 

It is usually convenient to restrict the choice of gauge so that the last term will vanish this can always be done because any part of A that is expressible as the gradient of some scalar field f (see p. 358) makes zero contribution to B. The scalar field may be chosen in such a way that p-A = (h/i) divA = 0, and this choice defines the coulomb gauge. Thus... 

On the other hand, there is also no fundamental problem with restricting RDFT to the Coulomb or Coulomb-Breit level. Choosing the Feynman gauge as used for the Hamiltonian (4.1), the full D is explicitly given by... 

Even after the introduction of the no-pair approximation the physical background of the RDFT formalism outlined in this Section is not yet identical with that of the standard methods based on the no-pair DC- or DCB-Hamiltonian. In RDFT the complete electron-electron interaction via the photon propagator is taken into account both in the Hartree energy (58) and in the construction of approximations for Exc (see Appendix C). On the other hand, there is also no fundamental problem in restricting RDFT to the Coulomb or Coulomb-Breit level. Choosing Feynman gauge, the full D y, Eqs.(201),(202), reduces to... 

Summation over the single-particle states is restricted to positive energy contributions, which has become known as the no virtual pair approximation. In practice, the interaction vu may be the complete energy-dependent, covariant interaction, vf2, the Coulomb interaction, gi2, or the transverse-gauge Breit operator, 312 -I- 612-... 

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