where H ^ ^ D ( i ) = [ q i ϕ ϕ ( r i ) + c ∑ ∑ s = x , y , z α α s ( i ) π π s ( I ) + α α 0 ( I ) m 0 c 2 ] is the Dirac Hamiltonian (see Dirac equation) for particle i at position r i and ϕ ϕ ( r i ) is the scalar potential at that position; q i is the charge of the particle, thus for electrons q i = − e. The one-electron Dirac Hamiltonians of the particles, along with their instantaneous Coulomb interactions 1/ r ij, form the Dirac–Coulomb operator. To this, Breit added the operator (now known as the (frequency-independent) Breit operator): B ^ ^ i j = − − 1 2 r i j [ α α → → ( i ) ⋅ ⋅ α α → → ( j ) + ( α α → → ( i ) ⋅ ⋅ r i j ) ( α α → → ( j ) ⋅ ⋅ r i j ) r i j 2 ] , where the Dirac matrices for electron i : α (i) = [ α x (i), α y (i), α z (i)]. The two terms in the Breit operator account for retardation effects to the first order. The wave function Ψ in the Breit equation is a spinor with 4 elements, since each electron is described by a Dirac bispinor with 4 elements as in the Dirac equation, and the total wave function is the tensor product of these.