24 research outputs found
The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes
This work considers the way that quantum loop effects modify the propagation
of light in curved space. The calculation of the refractive index for scalar
QED is reviewed and then extended for the first time to QED with spinor
particles in the loop. It is shown how, in both cases, the low frequency phase
velocity can be greater than c, as found originally by Drummond and Hathrell,
but causality is respected in the sense that retarded Green functions vanish
outside the lightcone. A "phenomenology" of the refractive index is then
presented for black holes, FRW universes and gravitational waves. In some
cases, some of the polarization states propagate with a refractive index having
a negative imaginary part indicating a potential breakdown of the optical
theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph
The Refractive Index of Curved Spacetime: the Fate of Causality in QED
It has been known for a long time that vacuum polarization in QED leads to a
superluminal low-frequency phase velocity for light propagating in curved
spacetime. Assuming the validity of the Kramers-Kronig dispersion relation,
this would imply a superluminal wavefront velocity and the violation of
causality. Here, we calculate for the first time the full frequency dependence
of the refractive index using world-line sigma model techniques together with
the Penrose plane wave limit of spacetime in the neighbourhood of a null
geodesic. We find that the high-frequency limit of the phase velocity (i.e. the
wavefront velocity) is always equal to c and causality is assured. However, the
Kramers-Kronig dispersion relation is violated due to a non-analyticity of the
refractive index in the upper-half complex plane, whose origin may be traced to
the generic focusing property of null geodesic congruences and the existence of
conjugate points. This puts into question the issue of micro-causality, i.e.
the vanishing of commutators of field operators at spacelike separated points,
in local quantum field theory in curved spacetime.Comment: 43 pages, 19 figures, JHEP3, conclusions respecting microcausality
modifie
Unconventional Gravitational Excitation of a Schwarzschild Black Hole
Besides the well-known quasinormal modes, the gravitational spectrum of a
Schwarzschild black hole also has a continuum part on the negative imaginary
frequency axis. The latter is studied numerically for quadrupole waves. The
results show unexpected striking behavior near the algebraically special
frequency . This reveals a pair of unconventional damped modes very
near , confirmed analytically.Comment: REVTeX4, 4pp, 6 EPS figure files. N.B.: "Alec" is my first, and
"Maassen van den Brink" my family name. v2: better pole placement in Fig. 1.
v3: fixed Refs. [9,20]. v4: added context on "area quantum" research; trimmed
one Fig.; textual clarification
The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index
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.Comment: 54 pages, 19 figures, corrected some signs in formulae and graph
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Finite- N effects for ideal polymer chains near a flat impenetrable wall
This paper addresses the statistical mechanics of ideal polymer chains next to a hard wall. The principal quantity of interest, from which all monomer densities can be calculated, is the partition function, G N(z) , for a chain of N discrete monomers with one end fixed a distance z from the wall. It is well accepted that in the limit of infinite N , G N(z) satisfies the diffusion equation with the Dirichlet boundary condition, G N(0) = 0 , unless the wall possesses a sufficient attraction, in which case the Robin boundary condition, G N(0) = - x G N ′(0) , applies with a positive coefficient, x . Here we investigate the leading N -1/2 correction, D G N(z) . Prior to the adsorption threshold, D G N(z) is found to involve two distinct parts: a Gaussian correction (for z <~Unknown control sequence '\lesssim' aN 1/2 with a model-dependent amplitude, A , and a proximal-layer correction (for z <~Unknown control sequence '\lesssim' a described by a model-dependent function, B(z)
Observation of magnetic order in the heavy-fermion superconductor UBe
We have measured the magnetostriction L(H) of a single crystal of the heavy-fermion superconductor UBe13 using an all-silicon high-precision capacitance dilatometer. We find clear evidence for a transition to an antiferromagnetic state at TN 8.8 K, which is suppressed in a field by dTN/dH 0.36 K/T. At low temperatures we observe pronounced magnetostrictive oscillations, which we believe are de Haasvan Alphen oscillations due to an unusual aspect of the Fermi surface. © 1990 The American Physical Society