I know this is really stupid. But bear with me.
In everything I have read so far, the Self Consistent Field (SCF) is always used to describe a method or a process, namely, that of iteratively solving the Schrodinger's Equation to generate new wavefunctions, using them for a new potential, and solving until convergence.
If SCF is not an actual field, why is it named as such? And then when we describe the SCF space what are we really talking about? Does the iterative process create a series of objects that spans a field?
For SCF: https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method or if you want a textbook for reference, there's always Szabo and Ostlund's Modern Quantum Chemistry.