2007/01/19 by G. M. Shore, G.M. Shore · 8 citations
Mathematics · Physics and Astronomy · #Atomic and Subatomic Physics Research #Causality (physics) #Cold Atom Physics and Bose-Einstein Condensates #Dispersion relation #Field (mathematics) #Field theory (psychology) #Gravitational field #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Negative energy #Null (SQL) #Physics #Quantum electrodynamics #Quantum field theory #Quantum mechanics #Quantum optics and atomic interactions #Superluminal motion #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.03.034
published as Nucl.Phys.B778:219-258,2007 · 42 pages, 14 figures
arxiv created 2007/01/19 · openalex publication_date 2007/04/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation of these constraints implies superluminal propagation, in the sense that the low-frequency limit of the phase velocity v\rm ph(0) exceeds c. It is explained why causality is related not to v\rm ph(0) but to the high-frequency limit v\rm ph(∞) and how these are related by the Kramers-Kronig dispersion relation, depending on the sign of the imaginary part of the refractive index \Ima n(\w) which is normally assumed positive. Superluminal propagation and its relation to UV completion is investigated in detail in three theories: QED in a background electromagnetic field, where the full dispersion relation for n(\w) is evaluated numerically for the first time and the role of the null energy condition T\m\nk^\m k^\n ≥ 0 is highlighted; QED in a background gravitational field, where examples of superluminal low-frequency phase velocities arise in violation of the positivity constraints; and light propagation in coupled laser-atom Ł-systems exhibiting Raman gain lines with \Ima n(\w) < 0. The possibility that a negative \Ima n(\w) must occur in quantum field theories involving gravity to avoid causality violation, and the implications for the relation of IR effective field theories to their UV completion, are carefully analysed.