``Faster than Light'' Photons in Gravitational Fields -- Causality, Anomalies and Horizons

A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions induced by vacuum polarisation in QED in curved spacetime. Two general theorems are presented: first, a polarisation sum rule which relates the polarisation averaged velocity shift to the matter energy-momentum tensor and second, a `horizon theorem' which ensures that the geometric event horizon for black hole spacetimes remains a true horizon for real photon propagation in QED. A comparision is made with the equivalent results for electromagnetic birefringence and possible connections between superluminal photon propagation, causality and the conformal anomaly are exposed.Comment: 15 pages, Plain Te

Automatically generating Feynman rules for improved lattice field theories

Deriving the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially when improvement terms are present. This physically important task is, however, suitable for automation. We describe a flexible algorithm for generating Feynman rules for a wide range of lattice field theories including gluons, relativistic fermions and heavy quarks. We also present an efficient implementation of this in a freely available, multi-platform programming language (\python), optimised to deal with a wide class of lattice field theories

A Local Effective Action for Photon-Gravity Interactions

Quantum phenomena such as vacuum polarisation in curved spacetime induce interactions between photons and gravity with quite striking consequences, including the violation of the strong equivalence principle and the apparent prediction of `superluminal' photon propagation. These quantum interactions can be encoded in an effective action. In this paper, we extend previous results on the effective action for QED in curved spacetime due to Barvinsky, Vilkovisky and others and present a new, local effective action valid to all orders in a derivative expansion, as required for a full analysis of the quantum theory of high-frequency photon propagation in gravitational fields.Comment: 22 pages, 9 figures, harvmac Te

`Faster than light' photons and rotating black holes

The effective action for QED in curved spacetime includes equivalence principle violating interactions between the electromagnetic field and the spacetime curvature. These interactions admit the possibility of superluminal yet causal photon propagation in gravitational fields. In this paper, we extend our analysis of photon propagation in gravitational backgrounds to the Kerr spacetime describing a rotating black hole. The results support two general theorems -- a polarisation sum rule and a `horizon theorem'. The implications for the stationary limit surface bounding the ergosphere are also discussed.Comment: Plain TeX, 12 pages, 1 figur

Faster than Light Photons in Gravitational Fields II - Dispersion and Vacuum Polarisation

Vacuum polarisation in QED in a background gravitational field induces interactions which effectively violate the strong equivalence principle and affect the propagation of light. In the low frequency limit, Drummond and Hathrell have shown that this mechanism leads to superluminal photon velocities. To confront this phenomenon with causality, however, it is necessary to extend the calculation of the phase velocity \vp(\w) to high frequencies, since it is \vp(\infty) which determines the characteristics of the effective wave equation and thus the causal structure. In this paper, we use a recently constructed expression, valid to all orders in a derivative expansion, for the effective action of QED in curved spacetime to determine the frequency dependence of the phase velocity and investigate whether superluminal velocities indeed persist in the high frequency limit.Comment: 27 pages, 7 figures, TeX with harvma

Leptogenesis and gravity: Baryon asymmetry without decays

A popular class of theories attributes the matter-antimatter asymmetry of the Universe to CP-violating decays of super-heavy BSM particles in the Early Universe. Recently, we discovered a new source of leptogenesis in these models, namely that the same Yukawa phases which provide the CP violation for decays, combined with curved-spacetime loop effects, lead to an entirely new gravitational mechanism for generating an asymmetry, driven by the expansion of the Universe and independent of the departure of the heavy particles from equilibrium. In this Letter, we build on previous work by analysing the full Boltzmann equation, exploring the full parameter space of the theory and studying the time-evolution of the asymmetry. Remarkably, we find regions of parameter space where decays play no part at all, and where the baryon asymmetry of the Universe is determined solely by gravitational effects.Comment: Journal version, published in Phys. Lett.

Superluminality and UV Completion

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 $v_{\rm ph}(\infty)$ 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\n}k^\m k^\n \ge 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 \L-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.Comment: 42 pages, 14 figure

Comments on "Note on varying speed of light theories"

In a recent note Ellis criticizes varying speed of light theories on the grounds of a number of foundational issues. His reflections provide us with an opportunity to clarify some fundamental matters pertaining to these theories

Light propagation in non-trivial QED vacua

Within the framework of effective action QED, we derive the light cone condition for homogeneous non-trivial QED vacua in the geometric optics approximation. Our result generalizes the ``unified formula'' suggested by Latorre, Pascual and Tarrach and allows for the calculation of velocity shifts and refractive indices for soft photons travelling through these vacua. Furthermore, we clarify the connection between the light velocity shift and the scale anomaly. This study motivates the introduction of a so-called effective action charge that characterizes the velocity modifying properties of the vacuum. Several applications are given concerning vacuum modifications caused by, e.g., strong fields, Casimir systems and high temperature.Comment: 13 pages, REVTeX, 3 figures, to appear in Phys. Rev.

Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature