Spinfoams in the holomorphic representation

We study a holomorphic representation for spinfoams. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann coherent state transform. We derive the expression of the 4d spinfoam vertex for Euclidean and for Lorentzian gravity in the holomorphic representation. The advantage of this representation rests on the fact that the variables used have a clear interpretation in terms of a classical intrinsic and extrinsic geometry of space. We show how the peakedness on the extrinsic geometry selects a single exponential of the Regge action in the semiclassical large-scale asymptotics of the spinfoam vertex.Comment: 10 pages, 1 figure, published versio

Primordial helium recombination. I. Feedback, line transfer, and continuum opacity

Precision measurements of the cosmic microwave background temperature anisotropy on scales ℓ>500 will be available in the near future. Successful interpretation of these data is dependent on a detailed understanding of the damping tail and cosmological recombination of both hydrogen and helium. This paper and two companion papers are devoted to a precise calculation of helium recombination. We discuss several aspects of the standard recombination picture, and then include feedback, radiative transfer in He i lines with partial redistribution, and continuum opacity from H i photoionization. In agreement with past calculations, we find that He ii recombination proceeds in Saha equilibrium, whereas He i recombination is delayed relative to Saha due to the low rates connecting excited states of He i to the ground state. However, we find that at z<2200 the continuum absorption by the rapidly increasing H i population becomes effective at destroying photons in the He i 21Po-11S line, causing He i recombination to finish around z≃1800, much earlier than previously estimated

QED cascades induced by circularly polarized laser fields

The results of Monte-Carlo simulations of electron-positron-photon cascades initiated by slow electrons in circularly polarized fields of ultra-high strength are presented and discussed. Our results confirm previous qualitative estimations [A.M. Fedotov, et al., PRL 105, 080402 (2010)] of the formation of cascades. This sort of cascades has revealed the new property of the restoration of energy and dynamical quantum parameter due to the acceleration of electrons and positrons by the field and may become a dominating feature of laser-matter interactions at ultra-high intensities. Our approach incorporates radiation friction acting on individual electrons and positrons.Comment: 13 pages, 10 figure

Shape Invariance in the Calogero and Calogero-Sutherland Models

We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the possibility of solving these models using algebraic methods based on this shape invariance. Our representation gives us a natural way to construct supersymmetric generalizations of these models, which are interesting both in their own right and for the insights they offer in connection with the exact solubility of these models.Comment: Latex file, 23 pages, no picture

Radiative transfer effects in primordial hydrogen recombination

The calculation of a highly accurate cosmological recombination history has been the object of particular attention recently, as it constitutes the major theoretical uncertainty when predicting the angular power spectrum of Cosmic Microwave Background anisotropies. Lyman transitions, in particular the Lyman-alpha line, have long been recognized as one of the bottlenecks of recombination, due to their very low escape probabilities. The Sobolev approximation does not describe radiative transfer in the vicinity of Lyman lines to a sufficient degree of accuracy, and several corrections have already been computed in other works. In this paper, the impact of some previously ignored radiative transfer effects is calculated. First, the effect of Thomson scattering in the vicinity of the Lyman-alpha line is evaluated, using a full redistribution kernel incorporated into a radiative transfer code. The effect of feedback of distortions generated by the optically thick deuterium Lyman-alpha line blueward of the hydrogen line is investigated with an analytic approximation. It is shown that both effects are negligible during cosmological hydrogen recombination. Secondly, the importance of high-lying, non overlapping Lyman transitions is assessed. It is shown that escape from lines above Ly-gamma and frequency diffusion in Ly-beta and higher lines can be neglected without loss of accuracy. Thirdly, a formalism generalizing the Sobolev approximation is developed to account for the overlap of the high-lying Lyman lines, which is shown to lead to negligible changes to the recombination history. Finally, the possibility of a cosmological hydrogen recombination maser is investigated. It is shown that there is no such maser in the purely radiative treatment presented here.Comment: 23 pages, 4 figures, to be submitted to PR

Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity

In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model seems the most promising. Here, we study its boundary states and introduce cylindrical functions on both the Lorentz connection and the time normal to the studied hypersurface. We call them projected cylindrical functions and we explain how they would naturally arise in a covariant formulation of Loop Quantum Gravity.Comment: Latex, 15 page

The twistorial structure of loop-gravity transition amplitudes

The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial description, which brings new light on both classical and quantum aspects of the theory. At the classical level, we clarify the covariant properties of the discrete geometries involved, and the role of the simplicity constraints in leading to SU(2) Ashtekar-Barbero variables. We identify areas and Lorentzian dihedral angles in twistor space, and show that they form a canonical pair. The primary simplicity constraints are solved by simple twistors, parametrized by SU(2) spinors and the dihedral angles. We construct an SU(2) holonomy and prove it to correspond to the (lattice version of the) Ashtekar-Barbero connection. We argue that the role of secondary constraints is to provide a non trivial embedding of the cotangent bundle of SU(2) in the space of simple twistors. At the quantum level, a Schroedinger representation leads to a spinorial version of simple projected spin networks, where the argument of the wave functions is a spinor instead of a group element. We rewrite the Liouville measure on the cotangent bundle of SL(2,C) as an integral in twistor space. Using these tools, we show that the Engle-Pereira-Rovelli-Livine transition amplitudes can be derived from a path integral in twistor space. We construct a curvature tensor, show that it carries torsion off-shell, and that its Riemann part is of Petrov type D. Finally, we make contact between the semiclassical asymptotic behaviour of the model and our construction, clarifying the relation of the Regge geometries with the original phase space.Comment: 40 pages, 3 figures. v2: minor improvements, references adde

Equivalence of the super Lax and local Dunkl operators for Calogero-like models

Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax operators for the Calogero and Sutherland models can be expressed in terms of the supercharges and so called local Dunkl operators constructed in our recent paper with M. Ioffe. Several important relations involving Lax matrices and Hamiltonians of the Calogero and Sutherland models are easily derived from the properties of Dunkl operators.Comment: 25 pages, Latex, no figures. Accepted for publication in: Jounal of Physics A: Mathematical and Genera