出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We discuss signatures of bound-state formation in finite volume via the L¨uscher finite size method.
Assuming that the phase-shift formula in this method inherits all aspects of the quantum scattering
theory, we may expect that the bound-state formation induces the sign of the scattering length to
be changed. If it were true, this fact provides us a distinctive identification of a shallow bound state
even in finite volume through determination of whether the second lowest energy state appears
just above the threshold. We also consider the bound-state pole condition in finite volume, based
on L¨uscher’s phase-shift formula and then find that the condition is fulfilled only in the infinite
volume limit, but its modification by finite size corrections is exponentially suppressed by the
spatial lattice size L. These theoretical considerations are also numerically checked through lattice
simulations to calculate the positronium spectrum in compact scalar QED, where the short-range
interaction between an electron and a positron is realized in the Higgs phase.
