Self-consistent Hartree-Fock approach to Phase Transitions

Hartree-Fock approach to Phase Transitions

Hartree-Fock in second quantized form

$\nu ={\frac {1}{2}}\sum _{\sigma \sigma ^{\prime }}\int d^{3}rd^{3}r^{\prime }v({\vec {r}}-{\vec {r^{\prime }}})\psi _{\sigma }^{\dagger }({\vec {r}})\psi _{\sigma ^{\prime }}^{\dagger }({\vec {r^{\prime }}})\psi _{\sigma ^{\prime }}({\vec {r^{\prime }}})\psi _{\sigma }({\vec {r}})$