116894284
The cauchy problem for non-linear Klein-Gordon equations
We consider in ℝn+1,n≧2, the non-linear Klein-Gordon equation. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincaré covariant then the non-linear representation of the Poincaré Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincaré group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincaré group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra.
119881917
Linearization of relativistic nonlinear wave equations
Some linearization theorems for relativistic nonlinear wave equations are formulated and proved. Examples are discussed and the physical meaning of such a linearization is sketched. Finally, some remarks concerning gauge theories are presented.
122026820
Field Theory on Curved Space Time and the TCP Theorem
A generalization is given to the Wightman axioms of field theory which permits to treat gravitational field as a Wightman field. This generalization permits to deduce TCP theorem for the gravitational field. The note ends with some critical remarks concerning the physical interpretation of the TCP theorem.
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.
121784848
On global solutions of the Maxwell-Dirac equations
We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.
125747217
NEXT, a HPXe TPC for neutrinoless double beta decay searches
The next-generation experiments for neutrinoless double b eta decay searches are a major challenge, since the detectors have to fulfill conflicting requir ements: they have to be very massive and scalable; very sensitive to the signature of the β β processes, and simultaneously impose extremely stringent limits on the copious backgrounds. A high-pressure gaseous Xenon TPC may be the ideal detector f or this purpose: the isotope 136Xe is almost 9% of natural Xenon and enrichment by centrifugati on is a relatively easy technology as demonstrated by the EXO collaboration; the detector can be e xtrapolated to large masses; energy resolution in gas is expected to be at the level of 1% FWHM at Qβ β ; this fact, combined with the very long life of theβ β 2ν mode accounts for negligible backgrounds of intrinsic orig in up to masses of the order of 1 ton. The detector is fully active an d the gas can be continuously re-circulated and purified, which, together with the existe nce of a kinematical signature gives an extra handle against backgrounds. NEXT (Neutrino Experiment with a Xenon TPC) is an on-going pr oject that aims to build a 100 kg HPXe TPC at a pressure of ∼10 bar. The experiment has already been aproved by the scient ifi committee of the Canfranc Underground Laboratory (LSC), in Spain, for the initial R&D phase. The NEXT Collaboration has defined an ambitious roadmap for t he next five years: an initial phase of R&D during 2 years will be used to decide the technolo gy (MicroMegas, GEMs, APDs, PMTs, etc.); in 3 years a first prototype (NEXT-10) will be con structed; followed by NEXT-100 in 5 years. A special grant (Consolider-Ingenio 2010) from t he Ministry of Science of Spain will fund the experiment during this period. The Collaboration i s composed by the leading Spanish groups in experimental neutrino and underground physics. The general ideas behind neutrinoless double beta decay sea rches with a HPXe TPC are discussed in this note.
118845292
The Relaxed Three-Algebras: Their Matrix Representation and Implications for Multi M2-brane Theory
We argue that one can relax the requirements of the non-associative threealgebras recently used in constructing D = 3 N = 8 superconformal field theories, and introduce the notion of “relaxed three-algebras”. We present a specific realization of the relaxed three-algebras in terms of classical Lie algebras with a matrix representation, endowed with a non-associative four-bracket structure which is prescribed to replace the three-brackets of the three-algebras. We show that both the so(4)-based solutions as well as the cases with non-positive definite metric find a uniform description in our setting. We discuss the implications of our four-bracket representation for the D = 3, N = 8 and multi M2-brane theory and show that our setup can shed light on the problem of negative kinetic energy degrees of freedom of the Lorentzian case.
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.
56350886
EXTREMAL BLACK HOLES, HOLOGRAPHY AND COARSE GRAINING
I review some of the concepts at the crossroads of gravitational thermodynamics, holography and quantum mechanics. First, the origin of gravitational thermodynamics due to coarse graining of quantum information is exemplified using the half-BPS sector of SYM and its LLM description in type IIB supergravity. The notion of black holes as effective geometries, its relation to the fuzzball programme and some of the puzzles raising for large black holes are discussed. Second, I review recent progress for extremal black holes, both microscopically, discussing a constituent model for stationary extremal non-BPS black holes, and semiclassically, discussing the extremal black hole/CFT conjecture. The latter is examined from the AdS3/CFT2 perspective. Third, I review the importance of the holographic principle to encode nonlocal gravity features allowing us to relate the gravitational physics of local observers with thermodynamics and the role causality plays in these arguments by identifying horizons (screens) as diathermic walls. I speculate with the emergence of an approximate CFT in the deep IR close to any horizon and its relation with an effective dynamical description of the degrees of freedom living on these holographic screens.
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.