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arXiv · hep-th/0107240

Microcausality and Energy-Positivity in all frames imply Lorentz Invariance of dispersion laws

Jacques Bros·Henri Epstein
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Abstract

A new presentation of the Borchers-Buchholz result of the Lorentz-invariance of the energy-momentum spectrum in theories with broken Lorentz symmetry is given in terms of properties of the Green's functions of microcausal Bose and Fermi-fields. Strong constraints based on complex geometry phenomenons are shown to result from the interplay of the basic principles of causality and stability in Quantum Field Theory: if microcausality and energy-positivity in all Lorentz frames are satisfied, then it is unavoidable that all stable particles of the theory be governed by Lorentz-invariant dispersion laws: in all the field sectors, discrete parts outside the continuum as well as the thresholds of the continuous parts of the energy-momentum spectrum, with possible holes inside it, are necessarily represented by mass-shell hyperboloids (or the light-cone). No violation of this geometrical fact can be produced by spontaneous breaking of the Lorentz symmetry.

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Jacques Bros, Henri Epstein. 2001-07-27. Microcausality and Energy-Positivity in all frames imply Lorentz Invariance of dispersion laws. https://doi.org/10.1103/physrevd.65.085023

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