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Register a new userThe Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index
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The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.
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In recent years a very exciting and intense activity has been devoted to the understanding and construction of materials that enjoy exotic optical properties, such as a negative refractive index. Motivated by these experimental and theoretical developments, we use the string-inspired idea of holography to study the electromagnetic response of a certain class of media: strongly coupled relativistic systems that admit a dual gravitational description. Our results indicate that this type of media generally have a negative refractive index. Moreover we observe that a negative refractive index could be a common feature of relativistic hydrodynamic systems at low frequencies.
Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observers frame.
Using the observed time and spatial intervals defined originally by Einstein and the observation frame in the vierbein formalism, we propose that in curved spacetime, for a wave received in laboratories, the observed frequency is the changing rate of the phase of the wave relative to the local observable time scale and the momentum the changing rate of the phase relative to the local observable spatial length scale. The case of Robertson-Walker universe is especially considered.
A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski spacetime and introduces a framework for studing in a precise manner membranes behavior near the black hole horizon and on the other hand, introduces a more general framework for examining the stability of topological defects in curved spacetimes.
We study a free scalar field $phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(Box)phi =0$, where $F$ is a polynomial of the form $F(Box)= prod_i (Box-m_i^2)$ and all masses $m_i$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantisation and briefly discuss the issue of negative energy versus negative norm and its relation to Reflection Positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish non-existence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background, and show how the Hubble friction may eliminate what would otherwise be unstable behaviour when interactions are included.
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