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arXiv · hep-th/0204118

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

J. Bros·H. 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, even if the field-theoretical framework is enlarged so as to include short-distance singularities wilder than distributions.

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J. Bros, H. Epstein. 2002-04-15. Microcausality and Energy-Positivity in all frames imply Lorentz Invariance of dispersion laws. https://arxiv.org/abs/hep-th/0204118

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