Abstract
Due to polarization effects, the massM of a stable particle in a quantum field theory enclosed in a large (space-like) box of sizeL and periodic boundary conditions in general differs from its infinite volume valuem. AsL increases, the finite size mass shift Δm =M−m goes to zero exponentially with a rate, which depends on the particle considered and on the spectrum of light particles in the theory. This behaviour follows from an apparently universal asymptotic formula, already presented earlier, which relates Δm to certain forward elastic scattering amplitudes. A detailed proof of this basic relation is given here to all orders of perturbation theory in arbitrary massive quantum field theories.
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Communicated by G. Mack
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Lüscher, M. Volume dependence of the energy spectrum in massive quantum field theories. Commun.Math. Phys. 104, 177–206 (1986). https://doi.org/10.1007/BF01211589
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DOI: https://doi.org/10.1007/BF01211589