Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator (MPDO) valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.Comment: v1: 11 pages, 1 figure. v2: very minor changes. About to appear in Journal of Mathematical Physic

The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex

Some components of the graviton two-point function have been recently computed in the context of loop quantum gravity, using the spinfoam Barrett-Crane vertex. We complete the calculation of the remaining components. We find that, under our assumptions, the Barrett-Crane vertex does not yield the correct long distance limit. We argue that the problem is general and can be traced to the intertwiner-independence of the Barrett-Crane vertex, and therefore to the well-known mismatch between the Barrett-Crane formalism and the standard canonical spin networks. In a companion paper we illustrate the asymptotic behavior of a vertex amplitude that can correct this difficulty.Comment: 31 page

Path Integral Approach to Residual Gauge Fixing

In this paper we study the question of residual gauge fixing in the path integral approach for a general class of axial-type gauges including the light-cone gauge. We show that the two cases -- axial-type gauges and the light-cone gauge -- lead to very different structures for the explicit forms of the propagator. In the case of the axial-type gauges, fixing the residual symmetry determines the propagator of the theory completely. On the other hand, in the light-cone gauge there is still a prescription dependence even after fixing the residual gauge symmetry, which is related to the existence of an underlying global symmetry.Comment: revtex 13pages, slightly expanded discussion, version to be published in Physical Review

The Case for Optically-Thick High Velocity Broad Line Region Gas in Active Galactic Nuclei

A combined analysis of the profiles of the main broad quasar emission lines in both Hubble Space Telescope and optical spectra shows that while the profiles of the strong UV lines are quite similar, there is frequently a strong increase in the Ly-alpha/H-alpha ratio in the high-velocity gas. We show that the suggestion that the high velocity gas is optically-thin presents many problems. We show that the relative strengths of the high velocity wings arise naturally in an optically-thick BLR component. An optically-thick model successfully explains the equivalent widths of the lines, the Ly-alpha/H-alpha ratios and flatter Balmer decrements in the line wings, the strengths of CIII] and the lambda 1400 blend, and the strong variability of high-velocity, high-ionization lines (especially HeII and HeI).Comment: 34 pages in AASTeX, including 10 pages of figures. Submitted to Astrophysical Journa

Three dimensional loop quantum gravity: physical scalar product and spin foam models

In this paper, we address the problem of the dynamics in three dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space--corresponding to the quantization of the infinite dimensional kinematical configuration space of the theory--to the physical Hilbert space. In particular, we provide the definition of the physical scalar product which can be represented in terms of a sum over (finite) spin-foam amplitudes. Therefore, we establish a clear-cut connection between the canonical quantization of three dimensional gravity and spin-foam models. We emphasize two main properties of the result: first that no cut-off in the kinematical degrees of freedom of the theory is introduced (in contrast to standard `lattice' methods), and second that no ill-defined sum over spins (`bubble' divergences) are present in the spin foam representation.Comment: Typos corrected, version appearing in Class. Quant. Gra

Models and experimental results from the wide aperture Nb-Ti magnets for the LHC upgrade

MQXC is a Nb-Ti quadrupole designed to meet the accelerator quality requirements needed for the phase-1 LHC upgrade, now superseded by the high luminosity upgrade foreseen in 2021. The 2-m-long model magnet was tested at room temperature and 1.9 K. The technology developed for this magnet is relevant for other magnets currently under development for the high-luminosity upgrade, namely D1 (at KEK) and the large aperture twin quadrupole Q4 (at CEA). In this paper we present MQXC test results, some of the specialized heat extraction features, spot heaters, temperature sensor mounting and voltage tap development for the special open cable insulation. We look at some problem solving with noisy signals, give an overview of electrical testing, look at how we calculate the coil resistance during at quench and show that the heaters are not working We describe the quench signals and its timing, the development of the quench heaters and give an explanation of an Excel quench calculation and its comparison including the good agreement with the MQXC test results. We propose an improvement to the magnet circuit design to reduce voltage to ground values by factor 2. The program is then used to predict quench Hot-Spot and Voltages values for the D1 dipole and the Q4 quadrupole.Comment: 8 pages, Contribution to WAMSDO 2013: Workshop on Accelerator Magnet, Superconductor, Design and Optimization; 15 - 16 Jan 2013, CERN, Geneva, Switzerlan

Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory

We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge configurations at non-zero temperature and compare periodic and anti-periodic temporal boundary conditions for the fermions. It is demonstrated that for the different boundary conditions often the modes are localized at different space-time points and have different sizes. Our observations are consistent with patterns expected for Kraan - van Baal solutions of the classical Yang-Mills equations. These solutions consist of constituent monopoles and the zero-modes are localized on different constituents for different boundary conditions. Our findings indicate that the excitations of the QCD vacuum are more structured than simple instanton-like lumps.Comment: Remarks added. To appear in Phys. Rev.

The loop-quantum-gravity vertex-amplitude

Spinfoam theories are hoped to provide the dynamics of non-perturbative loop quantum gravity. But a number of their features remain elusive. The best studied one -the euclidean Barrett-Crane model- does not have the boundary state space needed for this, and there are recent indications that, consequently, it may fail to yield the correct low-energy $n$-point functions. These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way certain second class constraints are imposed, arguably incorrectly, strongly. We present an alternative model, that can be derived as a bona fide quantization of a Regge discretization of euclidean general relativity, and where the constraints are imposed weakly. Its state space is a natural subspace of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network space. The model provides a long sought SO(4)-covariant vertex amplitude for loop quantum gravity.Comment: 6page

Motion in Quantum Gravity

We tackle the question of motion in Quantum Gravity: what does motion mean at the Planck scale? Although we are still far from a complete answer we consider here a toy model in which the problem can be formulated and resolved precisely. The setting of the toy model is three dimensional Euclidean gravity. Before studying the model in detail, we argue that Loop Quantum Gravity may provide a very useful approach when discussing the question of motion in Quantum Gravity.Comment: 30 pages, to appear in the book "Mass and Motion in General Relativity", proceedings of the C.N.R.S. School in Orleans, France, eds. L. Blanchet, A. Spallicci and B. Whitin