122340661
Wave operators and analytic solutions for systems of non-linear Klein-Gordon equations and of non-linear Schrödinger equations
We consider, in a 1+3 space time, arbitrary (finite) systems of nonlinear Klein-Gordon equations (respectively Schrödinger equations) with an arbitrary local and analytic non-linearity in the unknown and its first and second order space-time (respectively first order space) derivatives, having no constant or linear terms. No restriction is given on the frequency sign of the initial data. In the case of non-linear Klein-Gordon equations all masses are supposed to be different from zero.We prove, for such systems, that the wave operator (fromt=∞ tot=0) exists on a domain of small entire test functions of exponential type and that the analytic Cauchy problem, in ℝ+×ℝ3, has a unique solution for each initial condition (att=0) being in the image of the wave operator. The decay properties of such solutions are discussed in detail.
120008134
A wave operator for a non-linear Klein-Gordon equation
We prove the existence of a set of initial data to which correspond solutions of the nonlinear Klein-Gordon equation with a polynomial nonlinear term, which converge asymptotically, when t→+∞, to solutions of the linear Klein-Gordon equation.
119610987
Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations
Introduction The nonlinear representation $T$ and spaces of differentiable vectors The asymptotic nonlinear representation Construction of the approximate solution Energy estimates and $L^2-L^\infty$ estimates for the Dirac field Construction of the modified wave operator and its inverse Appendix.
119567009
Yang-Mills equations are formally linearizable
It is proved, in the framework of a recent theory of non-linear group representations elaborated by the authors, that the non-linear Yang-Mills equations are formally linearizable: there exists a formal non-linear operator which intertwins the non-linear Yang-Mills equations with their free (linear) part.
122293144
WIGHTMAN FORMULATION FOR THE QUANTIZATION OF THE GRAVITATIONAL FIELD.
122524343
A Garding domain for representations of some Hilbert Lie groups
AbstractGiven a Banach representation of a Hilbert Lie group, the Lie algebra 
$$\mathfrak{G}$$
 of which is the closure of the union of an increasing sequence of finite dimensional subalgebras, we construct a Gårding domain on which we differentiate the group representation to a representation of a dense subalgebra of 
$$\mathfrak{G}$$
.
13215290
Constraints on the redshift dependence of the dark energy potential
We develop a formalism to characterize the shape and the redshift evolution of the dark energy potential. Our formalism makes use of quantities similar to the horizon-flow parameters in inflation and is general enough that can deal with multiscalar quintessence scenarios, exotic matter components, and higher-order curvature corrections to General Relativity. We show how the shape of the dark energy potential can be recovered nonparametrically using this formalism and we present approximations analogous to the ones relevant to slow-roll inflation. Since presently available data do not allow a nonparametric and exact reconstruction of the potential, we consider a general parametric description. This reconstruction can also be used in other approaches followed in the literature (e.g., the reconstruction of the redshift evolution of the dark energy equation of state $w(z)$). Using observations of passively evolving galaxies and supernova data we derive constraints on the dark energy potential shape in the redshift range $0.1lzl1.8$. Our findings show that at the $1\ensuremath{\sigma}$ level the potential is consistent with being constant, although at the same level of confidence variations cannot be excluded with current data. We forecast constraints achievable with future data from the Atacama Cosmology Telescope.
119491620
Supersymmetric Kerr-Anti-de Sitter solutions
We prove the existence of one quarter supersymmetric type IIB configurations that arise as nontrivial scaling solutions of the standard five-dimensional Kerr-anti-de Sitter black holes by the explicit construction of its Killing spinors. This neutral, spinning solution is asymptotic to the static anti-de Sitter space-time with cosmological constant -(1/l{sup 2}), it has two finite equal angular momenta J{sub 1}={+-}J{sub 2}, mass M=(1/l)(|J{sub 1}|+|J{sub 2}|) and a naked singularity. We also address the scaling limit associated with one-half supersymmetric solution with only one angular momentum.
123342407
General relativity in a (2+1)-dimensional space-time: An electrically charged solution
AbstractWe have found a static electrically charged solution to the Einstein-Maxwell equations in a (2+1)-dimensional space-time. Studies of general relativity in lower dimensional space-times provide many new insights and a simplified arena for doing quantum mechanics. In (2+1)-dimensional space-time, solutions to the vacuum field equations are locally flat (point masses are conical sigularities), but when electromagnetic fields are presentTab≠O and the solutions are curved. For a static chargeQ we find
$$\mathop E\limits^ \to = Q\hat r/r$$
 andds2= −(kQ2/2π)In(rc/r)dt2 + (2π/kQ2[ln(rc/r)]−1dr2 +r2dφ2 whererc is a constant. There is a horizon atr =rc like the inner horizon of the Reisner-Nordström solution. We have produced a Kruskal extension of this metric which shows two static regions (I and III) withr rc. A spacelike slice across regions I and III shows a football-shaped universe with chargeQ at one end and −Q at the other. Slices in the dynamical regions (II and IV) show a cylindrical universe that is expanding in region II and contracting in region IV. Electromagnetic solutions to the Einstein-Maxwell field equations in lower dimensional space-times can be used to provide new insights into Kaluza-Klein theories. In terms of the Kaluza-Klein theory, for example, electromagnetic radiation in a (2+1)-dimensional space-time is really gravitational radiation in the associated (3+1)-dimensional Kaluza-Klein space-time. According to Kaluza Klein theory the absence of gravitational radiation in (2+1)-dimensional space-time implies (correctly) the absence of electromagnetic radiation in (1+1)-dimensional space-time.
119108532
Helical Luttinger Liquids and three dimensional black holes
We use the AdS/CFT correspondence to discuss an equivalence between a helical, strongly coupled Luttinger liquid and a fermion propagating in the background of a topologically charged black hole in three dimensions. The Fermi level is set by the topological charges, thus surmounting difficulties in low dimensions of the standard approach using Coulomb charged black holes. The construction is fully embeddable in string theory, and the microscopic Lagrangian is explicitly known. The retarded Green function at low temperature and energy arises from the geometry very near the black hole horizon, a structure that is universal for all cold, charged liquids with a dual $\mathbb{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}^{s}$ invariant description in gravity. This explains a subtle relationship between Luttinger physics and the infrared behavior of higher dimensional non-Fermi liquids in the AdS/CFT correspondence.
15296521
Null orbifolds in AdS, Time Dependence and Holography
We study M/D-branes in a null-brane background. By taking a near horizon limit, one is left with cosmological models in the corresponding Poincarpatches. To deal with their usual horizons, we either extend these models to global AdS or remain in the Poincarpatch and apply a T-duality transformation whenever the efiective radius of the compact dimension associated with the null-brane probes distances smaller than the string scale. The flrst scenario gives rise to null orbifolds in AdS spaces, which are described in detail. Their conformal boundaries are singular. The second has a dual gauge theory description in terms of Super Yang-Mills in the null-brane background. The latter is a good candidate for a non-perturbative deflnition of string theory in a time- dependent background.