Simulating many-body physics with quantum phase-space methods

Extended phase space−→ λ = (Ω,α,α + ,n,m,m + )=⇒ Hilbert-space dimension: 2 M for fermions, N M for bosons=⇒ phase-space dimension: 2(1−M +2M 2 ) for fermions, 2(1+3M +2M 2 )for bosons✄ Moments:〈 〉〈â i 〉 = E [α i ]â † i â j = E [ α + i α ]j + n i j〈â i â j 〉 = E [α i α j + m i j ]Simulating many-body physics with quantum phase-space methods 23