My background is in molecular physics, and I have encountered the term 'exchange interaction' in this context first, but it seems to be used in many areas of physics.
In my understanding, seems to be confirmed by this question or the Wikipedia page, exchange interaction is defined as the energy difference between exchanging two particles in the total wavefunction defined by one-particle orbitals. For example if we assume that the helium atom has the wavefunction (with proper normalization and antisymmetrization ensured by the operator $\hat{A}$)
$$ \Psi = \hat{A} [\psi_A(r_1) \psi_B(r_2)] \; , $$
then the total energy will have Coulomb $J$ and exchange $K$ contributions of the form
$$ J = \int \frac{(\psi_A(r_1) \psi_B(r_2))^2}{r_{12}} \; $$
$$ K = \int \frac{\psi_A(r_1) \psi_B(r_2) \psi_A(r_2) \psi_B(r_1) }{r_{12}} \; , $$
respectively, with $K$ called exchange due to the exchange of the electrons in the orbitals.
The full wavefunction $\Psi(r_1,r_2)$ will, of course, not be exactly factored into one-particle contributions, so the integrals $J$ and $K$ will not be defined as they have been above, and the total energy will just be $\langle \Psi|\hat{H}|\Psi\rangle $ without any specific contributions arising naturally.
My question is then: does it make sense to talk about exchange interaction in such cases? Does exchange interaction only arise from our assumption of one-particle orbitals, or is it somehow a fundamental concept of nature, defined even if the exact many-body wavefunction is known?
