  General analytic energy bounds are derived for N-boson systems governed by
semirelativistic Hamiltonians of the form
  H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a
static attractive pair potential. A translation-invariant model Hamiltonian H_c
is constructed. We conjecture that <H> \ge <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 formulas are
derived and compared with earlier bounds.
