Gravitational Collapse in Quantum Mechanics with Relativistic Kinetic Energy

摘要

We prove that the mechanical Hamiltonian H = sigma sub(i=1)sup(N) (p exp 2 + m exp 2 )sup(1/2) - kappa sigma sub(i>j) Vertical Barxsub(i) - xsub(j)Vertical Bar exp -1 for bosons (resp. fermions) is bounded from below if N <= csub(b) kappa exp -1 (resp. N <= csub(f) kappa sup(-3/2)). H is unbounded from below if N > csub(b)' kappa exp -1 (resp. N >= csub(f)' kappa sup(-3/2)). The constants csub(b) and csub(b)' (resp. csub(f) and csub(f)') differ by about a factor 2. (Atomindex citation 15:026506)