出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We determine the quantization condition for the energy levels of two interacting particles in a
finite box in a “moving frame”, i.e. one in which the total momentum of pions is non-zero. This
condition is valid up to corrections which fall exponentially withe the box size, and holds only
below the inelastic threshold. It is derived using field theoretic methods, using a generalization
of previous summation formulae relating sums and integrals over momenta. The result agrees
with that obtained earlier by Rummakainen and Gottlieb using a relativistic quantum mechanical
approach. Technically, we expand the finite-volume four-point Green function in terms of the
infinite-volume Bethe-Salpeter kernel, and determine the position of the poles. The final result
is written in terms of the two-pion scattering phase shift. Our result can be used to facilitate the
determination of the scattering phase shift, and can be used to generalize the Lellouch-Lüscher
formula relating finite-volume two-particle matrix elements to those in infinite volume.
