Relativistic \(N\)-particle energy shift in finite volume. (English) Zbl 1460.81066
Summary: 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.
MSC:
| 81T25 | Quantum field theory on lattices |
| 81T12 | Effective quantum field theories |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
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