The independent-electron model as a quantum field theory

An alternative interpretation of this equation is that y(t) is a time-dependent Lagrange multiplier, introduced to enforce constant normalization By the 

2 The independent-electron model as a quantum field theory 

The reference state t of A-electron theory becomes a reference vacuum state 4 ) in the field theory. A complete orthonormal set of spin-indexed orbital functions fip(x) is defined by eigenfunctions of a one-electron Hamiltonian Ti, with eigenvalues ep. The reference vacuum state corresponds to the ground state of a noninteracting A-electron system determined by this Hamiltonian. N occupied orbital functions (el pi) are characterized by fermion creation operators a such that a] t ) =0. Here pt is the chemical potential or Fermi level. A complementary orthogonal set of unoccupied orbital functions are characterized by destruction operators aa such that aa ) = 0 for ea p and a N. A fermion quantum field is defined in this orbital basis by 

The fermion creation and destruction operators are defined such that apa +a ap = Spq. In analogy to relativistic theory, and more appropriate to the linear response theory to be considered here, the elementary fermion operators ap can be treated as algebraic objects fixed in time, while the orbital functions are solutions of a time-dependent Schrodinger equation 

An (AH-l)-electron basis state is defined such that 4 ) = al 4 ) if a N. Here 

---