Notation

Some common notation we use in The nuclear many-body problem 🤯 and this section in general.

• We will use the shorthand p and h for particle and hole states, and also their combinations (i.e. pp, ph, hp, hh).
• For single particle subindices, we will use $i,j$ for hole states, $m,n$ for particle states and $k,l,p,q,r\dots$ for generic states. Note that $p$ will be used also exclusively when referring to paired particles in HF-Bogoliubov, which is a bit confusing.
• We will often use the "antisymmetrized potential", defined like so:$${\overline{v}}_{ab,cd}=v_{ab,cd}-v_{ab,dc}$$where$$v_{ab,cd}=⟨ab|v(1,2,3,4)|cd⟩$$and $v$ is the most general from of a two-particle potential.