Chemists often discuss sigma and pi bonds. To a physicist, it's not easy to figure out what these actually are, as discussions tend to be full of lots of chemistry jargon about "antibonding", "backbonding", "aromaticity", "ligands", "reactivity", etc. - terms which most physicists aren't familiar with. I suspect (although I'm not sure) that sigma and pi bonds are probably fairly easy to define precisely in terms of fundamental quantum-mechanical principles like wavefunctions, spherical harmonics, and symmetry groups that a physicist is more likely to be familiar with, and that the difficulty is mostly a language issue rather than a conceptual issue.
Is there a definition of sigma and pi bonds that uses a minimum of chemistry jargon (but as much physics jargon as necessary :-) )? Please state any assumptions explicitly - for example, chemists talk about "orbitals" a lot in a multi-electron context, so I assume they're pretty much always working in the Hartree-Fock approximation and neglecting inter-electron entanglement (but please correct me if I'm wrong).