Antoine Folacci

Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension

We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator

Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in higher-dimensional curved spacetime (in connection with the Hadamard regularization of the stress-energy tensor), we improve the DeWitt-Schwinger and Hadamard representations of the Feynman propagator of a massive scalar field theory defined on an arbitrary gravitational background by deriving higher-order terms for the covariant Taylor series expansions of the geometrical coefficients -- i.e., the DeWitt and Hadamard coefficients -- that define them.

Zero modes, Euclideanization, and quantization

We consider the massless scalar field on the four-dimensional sphere S 4 . Its classical action S=1/2∫ s4 dV(⊇φ) 2 , is degenerate under the global invariance φ→φ+const. We then quantize the massless scalar field as a gauge theory by constructing a Becchi-Rouet-Stora-Tyutin-invariant quantum action. The corresponding gauge-breaking term is a nonlocal one of the form S GB =(1/2αV)(∫ s4 dV φ) 2 where α is a gauge parameter and V is the volume of S 4

Universality of high-energy absorption cross sections for black holes

We consider the absorption problem for a massless scalar field propagating in static and spherically symmetric black holes of arbitrary dimension endowed with a photon sphere. For this wide class of black holes, we show that the fluctuations of the high energy absorption cross section are totally and very simply described from the properties (dispersion relation and damping) of the waves trapped near the photon sphere and therefore, in the eikonal regime, from the characteristics (orbital period and Lyapunov exponent) of the null unstable geodesics lying on the photon sphere. This is achieved by using Regge pole techniques. They permit us to make an elegant and powerful resummation of the absorption cross section and to extract then all the physical information encoded in the sum over the partial wave contributions. Our analysis induces moreover some consequences concerning Hawking radiation which we briefly report.

Surface polaritons on left-handed cylinders: A complex angular momentum analysis

We consider the scattering of electromagnetic waves by a left-handed cylinder -- i.e., by a cylinder fabricated from a left-handed material -- in the framework of complex angular momentum techniques. We discuss both the TE and TM theories. We emphasize more particularly the resonant aspects of the problem linked to the existence of surface polaritons. We prove that the long-lived resonant modes can be classified into distinct families, each family being generated by one surface polariton propagating close to the cylinder surface and we physically describe all the surface polaritons by providing, for each one, its dispersion relation and its damping. This can be realized by noting that each surface polariton corresponds to a particular Regge pole of the

Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress-energy tensor

S

Complex angular momentum in black hole physics and quasinormal modes

matrix of the cylinder. Moreover, for both polarizations, we find that there exists a particular surface polariton which corresponds, in the large-radius limit, to the surface polariton which is supported by the plane interface. There exists also an infinite family of surface polaritons of whispering-gallery type which have no analogs in the plane interface case and which are specific to left-handed materials.

Resonance and absorption spectra of the Schwarzschild black hole for massive scalar perturbations: A complex angular momentum analysis

We provide irreducible expressions for the metric variations of the gravitational action terms constructed from the 17 curvature invariants of order six in the derivatives of the metric tensor, i.e., from the geometrical terms appearing in the diagonal heat-kernel or Gilkey-DeWitt coefficient

Quasinormal modes of the BTZ black hole are generated by surface waves supported by its boundary at infinity

a_3

Whispering-gallery modes and resonances of an elliptic cavity

. We then express, for a four-dimensional spacetime, the approximated stress-energy tensor constructed from the renormalized DeWitt-Schwinger effective action associated with a massive scalar field. We also construct, for higher dimensional spacetimes, the infinite counterterms of order six in the derivatives of the metric tensor appearing on the left-hand side of Einstein equations as well as the contribution associated with the cubic Lovelock gravitational action. In the appendix, we provide a list of geometrical relations we have used and which are more generally helpful for calculations in two-loop quantum gravity in a four-dimensional background or for calculations in one-loop quantum gravity in higher dimensional background. We also obtain the approximated stress-energy tensors associated with a massive spinor field and a massive vector field propagating in a four-dimensional background.