Quantization of BMS3_3 orbits: a perturbative approach

We compute characters of the BMS group in three dimensions. The approach is the same as that performed by Witten in the case of coadjoint orbits of the Virasoro group in the eighties, within the large central charge approximation. The procedure involves finding a Poisson bracket between classical variables and the corresponding commutator of observables in a Hilbert space, explaining why we call this a quantization. We provide first a pedagogical warm up by applying the method to both SL(2,R) and Poincar\'{e}3 groups. As for BMS3, our results coincide with the characters of induced representations recently studied in the literature. Moreover, we relate the 'coadjoint representations' to the induced representations.Comment: 17 pages. v2: references added. v3: minor changes and published in Nucelar Physics

Quasilocal energy for three-dimensional massive gravity solutions with chiral deformations of AdS boundary conditions

We consider critical gravity in three dimensions; that is, the New Massive Gravity theory formulated about Anti-de Sitter (AdS) space with the specific value of the graviton mass for which it results dual to a two-dimensional conformal field theory with vanishing central charge. As it happens with Kerr black holes in four-dimensional critical gravity, in three-dimensional critical gravity the Banados-Teitelboim-Zanelli black holes have vanishing mass and vanishing angular momentum. However, provided suitable asymptotic conditions are chosen, the theory may also admit solutions carrying non-vanishing charges. Here, we give simple examples of exact solutions that exhibit falling-off conditions that are even weaker than those of the so-called Log-gravity. For such solutions, we define the quasilocal stress-tensor and use it to compute conserved charges. Despite the drastic deformation of AdS3 asymptotic, these solutions have finite mass and angular momentum.Comment: 7 pages. v3: Typos corrected. Version accepted for publicatio

Study of the phase transition in polycrystalline (Ba_{0.90}Pb_{0.10})(Ti_{0.90}Sn_{0.10})O_3

Polycrystalline sample of (Ba_{0.90}Pb_{0.10})(Ti_{0.90}Sn_{0.10})O_3 was obtained by means of a conventional ceramic technology. The dielectric measurements were performed depending on temperature and frequency of electric measuring field. The character of the phase transitions of (Ba_{0.90}Pb_{0.10})(Ti_{0.90}Sn_{0.10})O_3 ceramics strongly depends on the presence of Pb in the sample. The obtained results pointed out the diffused character of phase transition. The temperature dependence of the dielectric properties showed that the phase transition from the paraelectric phase to ferroelectric one takes place at the same temperature (T_{m}=367 K). It does not depend on the frequency of the measuring electric field. A change of the value of the parameter \gamma takes place in the paraelectric phase.Comment: 5 pages, 6 figure

Scalar field dynamics in a BTZ background with generic boundary conditions

The revisit the dynamics of a massive scalar field in a BTZ background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically-sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window −3/4≤m2eℓ2<0 can be well-defined within a one-parametric family of distinct boundary conditions (−3/4 being the conformally-coupled case), while for m2eℓ2≥0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m2eℓ2<−1, and also shown that in the range m2eℓ2∈[−1,−3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly in describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved.Fil: Garbarz, Alan Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: La Madrid, Joan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

Relative entropy of an interval for a massless boson at finite temperature

We compute Araki's relative entropy associated to a bounded interval $I=(a,b)$ between a thermal state and a coherent excitation of itself in the bosonic U(1)-current model, namely the (derivative of the) chiral boson. For this purpose we briefly review some recent results on the entropy of standard subspaces and on the relative entropy of non-pure states such as thermal states. In particular, recently Bostelmann, Cadamuro and Del Vecchio have obtained the relative entropy at finite temperature for the unbounded interval $(-\infty,t)$, using previous results of Borchers and Yngvason, mainly a unitary dilation that provides the modular evolution in the negative half-line. Here we find a unitary rotation in order to make use of the full PSL$(2,\mathbb{R})$ symmetries and obtain the modular group, modular Hamiltonian and the relative entropy $S$ of a bounded interval at finite temperature. Such relative entropy entails both a Bekenstein-like bound and a QNEC-like bound, but violates $S''\geq 0$. Finally, we extend the results to the free massless boson in $1+1$ dimensions with analogous bounds.Comment: 22 pages, 2 figure

Classification of boundary gravitons in AdS3 gravity

We revisit the description of the space of asymptotically AdS3 solutions of pure gravity in three dimensions with a negative cosmological constant as a collection of coadjoint orbits of the Virasoro group. Each orbit corresponds to a set of metrics related by diffeomorphisms which do not approach the identity fast enough at the boundary. Orbits contain more than a single element and this fact manifests the global degrees of freedom of AdS3 gravity, being each element of an orbit what we call boundary graviton. We show how this setup allows to learn features about the classical phase space that otherwise would be quite difficult. Most important are the proof of energy bounds and the characterization of boundary gravitons unrelated to BTZs and AdS3. In addition, it makes manifest the underlying mathematical structure of the space of solutions close to infinity. Notably, because of the existence of a symplectic form in each orbit, being this related with the usual Dirac bracket of the asymptotic charges, this approach is a natural starting point for the quantization of different sectors of AdS3 gravity. We finally discuss previous attempts to quantize coadjoint orbits of the Virasoro group and how this is relevant for the formulation of AdS3 quantum gravity.Facultad de Ciencias ExactasInstituto de Física La Plat

Comparative analysis of PHP frameworks on the example of Laravel and Symfony

This study aims to determine which of the analyzed PHP-based design patterns – Laravel or Symfony – is a better and more universal solution for a developer. For this purpose, a comparative analysis was carried out based on the available documentation, as well as a comparison of the static and dynamic metrics obtained in the research environment of both tested patterns. As a result of a series of experiments and studies, it was established that both design patterns are an optimal and efficient solution, but their best application depends on the developer's individual needs and project requirements

Mathematical modeling of phenomena of dynamic recrystallization during hot plastic deformation in high-carbon bainitic steel

Based on the research results, coefficients were determined in constitutive equations, describing the kinetics of dynamic recrystallization in high-carbon bainitic steel during hot deformation. The developed mathematical model takes into account the dependence of changing kinetics in the size evolution of the initial austenite grains, the value of strain, strain rate, temperature and time. Physical simulations were carried out on rectangular specimens measuring 10 × 15 × 20 mm. Compression tests with a plane state of deformation were carried out using a Gleeble 3800

Cylinder transition amplitudes in pure AdS3 gravity

A spacelike surface with cylinder topology can be described by various sets of canonical variables within pure AdS3 gravity. Each is made of one real coordinate and one real momentum. The Hamiltonian can be either H = 0 or it can be nonzero and we display the canonical transformations that map one into the other, in two relevant cases. In a choice of canonical coordinates, one of them is the cylinder aspect q, which evolves nontrivially in time. The time dependence of the aspect is an analytic function of time t and an “angular momentum” J. By analytic continuation in both t and J we obtain a Euclidean evolution that can be described geometrically as the motion of a cylinder inside the region of the 3D hyperbolic space bounded by two “domes” (i.e. half spheres), which is topologically a solid torus. We find that for a given J the Euclidean evolution cannot connect an initial aspect to an arbitrary final aspect; moreover, there are infinitely many Euclidean trajectories that connect any two allowed initial and final aspects. We compute the transition amplitude in two independent ways; first by solving exactly the time-dependent Schrödinger equation, then by summing in a sensible way all the saddle contributions, and we discuss why both approaches are mutually consistent.Fil: Garbarz, Alan Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Kim, Jayme. Montclair State University.; Estados UnidosFil: Porrati, Massimo. University of New York. Center for Cosmology and Particle Physics; Estados Unido

Conformal invariance and apparent universality of semiclassical gravity

In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike what happens in the case the coupling to the curvature \xi is generic, for the special cases \xi=0 and \xi = 1/6 the large distance behavior of the expectation value turns out to be independent of the internal structure of the gravitational source. Here, we address a higher dimensional generalization of this result: We first compute the difference between a black hole and a static spherically symmetric star for the observables and in the far field limit. Thus, we show that the conformally invariant massless scalar field theory in a static spherically symmetric background exhibits such universality phenomenon in D\geq 4 dimensions. Also, using the one-loop effective action, we compute for a weakly gravitating object. These results lead to the explicit expression of the expectation value for a Schwarzschild-Tangherlini black hole in the far field limit. As an application, we obtain quantum corrections to the gravitational potential in D dimensions, which for D=4 are shown to agree with the one-loop correction to the graviton propagator previously found in the literature.Comment: 11 page