Relativistic N-particle energy shift in finite volume

We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L-6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N-particle ground state energy shift in the complex phi (4) theory.

Automated summary

The paper presents a general method for deriving the energy shift of an interacting system of N spinless particles using nonrelativistic effective field theory, with relativistic corrections explicitly included. This method is applied to obtain the ground state of N particles and the first excited state of two and three particles to a certain order, based on the threshold parameters of relativistic scattering amplitudes. The resulting expressions are used to analyze the N-particle ground state energy shift in the complex phi (4) theory.