Binding energy of semirelativistic N-boson systems

General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=Sigma(N)(i=1)(p(i)(2) + m(2))(1/2 +) Sigma(N)(1=i >= < H-c > generally, and we prove this for N = 3, and for N = 4 when m = 0. The conjecture is also valid generally for the harmonic oscillator and in the nonrelativistic large-m limit. This formulation allows reductions to scaled 3- or 4-body problems, whose spectral bottoms provide energy lower bounds. The example of the ultrarelativistic linear potential is studied in detail and explicit upper-and lower-bound formulae are derived and compared with earlier bounds.