BF Actions for the Husain-Kuchar Model

We show that the Husain-Kuchar model can be described in the framework of BF theories. This is a first step towards its quantization by standard perturbative QFT techniques or the spin-foam formalism introduced in the space-time description of General Relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.Comment: 21 pages (in DIN A4 format), minor typos corrected; to appear in Phys. Rev.

Unitary evolution of free massless fields in de Sitter space-time

We consider the quantum dynamics of a massless scalar field in de Sitter space-time. The classical evolution is represented by a canonical transformation on the phase space for the field theory. By studying the corresponding Bogoliubov transformations, we show that the symplectic map that encodes the evolution between two instants of time cannot be unitarily implemented on any Fock space built from a SO(4)-symmetric complex structure. We will show also that, in contrast with some effectively lower dimensional examples arising from Quantum General Relativity such as Gowdy models, it is impossible to find a time dependent conformal redefinition of the massless scalar field leading to a quantum unitary dynamics.Comment: 20 pages. Comments and references adde

Hilbert space structure of covariant loop quantum gravity

We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum states are realized by a generalization of spin network states based on Lorentz Wilson lines projected on irreducible representations of an SO(3) subgroup. The problem of infinite dimensionality of the unitary Lorentz representations is absent due to this projection. Nevertheless, the projection preserves the Lorentz covariance of the Wilson lines so that the symmetry is not broken. Under certain conditions the states can be thought as functions on a homogeneous space. We define the inner product as an integral over this space. With respect to this inner product the spin networks form an orthonormal basis in the investigated sector. We argue that it is the only relevant part of a larger state space arising in the approach. The problem of the noncommutativity of the Lorentz connection is solved by restriction to the simple representations. The resulting structure shows similarities with the spin foam approach.Comment: 20 pages, RevTE

Accuracy of the LEP Spectrometer Beam Orbit Monitors

At the LEP e+/e- collider, a spectrometer is used to determine the beam energy with a target accuracy of 10-4. The spectrometer measures the lattice dipole bending angle of the beam using six beam position monitors (BPMs). The required calibration error imposes a BPM accuracy of a 10-6 m corresponding to a relative electrical signal variation of 2. 10-5. The operating parameters have been compared with beam simulator results and non-linearBPM response simulations. The relative beam current variations between 0.02 and 0.03 and position changes of 0.1 mm during the fills of last year lead to uncertainties in the orbit measurements of well below 10-6 m. For accuracy tests absolute beam currents were varied by a factor of three. The environment magnetical field is introduced to correct orbit readings. The BPM linearity and calibration was checked using moveable supports and wire position sensors. The BPM triplet quantity is used to determine the orbit position monitors accuracy. The BPM triplet changed during the fills between 1 and 2 10-6 m RMS, which indicates a single BPM orbit determination accuracy between 1 and 1.5 10-6 m

Is Barbero's Hamiltonian formulation a Gauge Theory of Lorentzian Gravity?

This letter is a critique of Barbero's constrained Hamiltonian formulation of General Relativity on which current work in Loop Quantum Gravity is based. While we do not dispute the correctness of Barbero's formulation of general relativity, we offer some criticisms of an aesthetic nature. We point out that unlike Ashtekar's complex SU(2) connection, Barbero's real SO(3) connection does not admit an interpretation as a space-time gauge field. We show that if one tries to interpret Barbero's real SO(3) connection as a space-time gauge field, the theory is not diffeomorphism invariant. We conclude that Barbero's formulation is not a gauge theory of gravity in the sense that Ashtekar's Hamiltonian formulation is. The advantages of Barbero's real connection formulation have been bought at the price of giving up the description of gravity as a gauge field.Comment: 12 pages, no figures, revised in the light of referee's comments, accepted for publication in Classical and Quantum Gravit

Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields

The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step towards their quantization. We will pay special attention to the coupling of matter and those features that arise for the three-handle and three-sphere topologies that are not present in the well studied three torus case -in particular the polar constraints that come from the regularity conditions on the metric. As a byproduct of our analysis we will get an alternative understanding, within the Hamiltonian framework, of the appearance of initial and final singularities for these models.Comment: Final version to appear in Classical and Quantum Gravit

Minisuperspace Examples of Quantization Using Canonical Variables of the Ashtekar Type: Structure and Solutions

The Ashtekar variables have been use to find a number of exact solutions in quantum gravity and quantum cosmology. We investigate the origin of these solutions in the context of a number of canonical transformations (both complex and real) of the basic Hamiltonian variables of general relativity. We are able to present several new solutions in the minisuperspace (quantum cosmology) sector. The meaning of these solutions is then discussed.Comment: 23 pages, latex, 3 figures (uuencoded, separate file

Performance of BPM Electronics for the LEP Spectrometer

At the LEP e+/e- collider at CERN, Geneva, a Spectrometer is used to determine the beam energy with a relative accuracy of 10-4. The Spectrometer measures the change in bending angle in a well-characterised dipole magnet as LEP is ramped. The beam trajectory is obtained using three beam position monitors (BPMs) on each side of the magnet. The error on each BPM measurement should not exceed 1 micron if the desired accuracy on the bending angle is to be reached. The BPMs used consist of an aluminium block with an elliptical aperture and four capacitive button pickup electrodes. The button signals are fed to customised electronics supplied by Bergoz. The electronics use time multiplexing of individual button signals through a single processing chain to optimise for long-term stability. We report on our experience of the performance of these electronics, describing measurements made with test signals and with beam. We have implemented a beam-based calibration procedure and have monitored the reproducibility of the measurements obtained over time. Measurements show that a relative accuracy better than 300 nm is achievable over a period of 1 hr

Dynamical Critical Phenomena and Large Scale Structure of the Universe: the Power Spectrum for Density Fluctuations

As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with time-- dependent viscosity in epochs of dissipation. As a consequence of the Dynamical Critical Scaling induced by noise and fluctuations, these equations describe the fractal behavior (with a scale dependent fractal dimension) observed at the smaller scales for the galaxy--to--galaxy correlation function and $also$ the Harrison--Zel'dovich spectrum at decoupling. By a Renormalization Group calculation of the two--point correlation function between galaxies in the presence of (i) the expansion of the Universe and (ii) non--equilibrium, we can account, from first principles, for the main features of the observed shape of the power spectrum.Comment: 13 pages with 2 encapsulated PostScript figures included, gzipped tar forma