Covariant Canonical Gauge theory of Gravitation resolves the Cosmological Constant Problem

The covariant canonical transformation theory applied to the relativistic theory of classical matter fields in dynamic space-time yields a new (first order) gauge field theory of gravitation. The emerging field equations embrace a quadratic Riemann curvature term added to Einstein's linear equation. The quadratic term facilitates a momentum field which generates a dynamic response of space-time to its deformations relative to de Sitter geometry, and adds a term proportional to the Planck mass squared to the cosmological constant. The proportionality factor is given by a dimensionless parameter governing the strength of the quadratic term. In consequence, Dark Energy emerges as a balanced mix of three contributions, (A)dS curvature plus the residual vacuum energy of space-time and matter. The Cosmological Constant Problem of the Einstein-Hilbert theory is resolved as the curvature contribution relieves the rigid relation between the cosmological constant and the vacuum energy density of matter

Canonical Transformation Path to Gauge Theories of Gravity

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De~Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the free gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics Hamiltonian" is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields -- this is beyond the Einstein-Hilbert theory of General Relativity.Comment: 16 page

Generalized Courant–Snyder theory and Kapchinskij–Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation, and reduces beam pulsation

Simulation of adiabatic thermal beams in a periodic solenoidal magnetic focusing field

Self-consistent particle-in-cell simulations are performed to verify earlier theoretical predictions of adiabatic thermal beams in a periodic solenoidal magnetic focusing field [ K. R. Samokhvalova, J. Zhou and C. Chen Phys. Plasmas 14 103102 (2007); J. Zhou, K. R. Samokhvalova and C. Chen Phys. Plasmas 15 023102 (2008)]. In particular, results are obtained for adiabatic thermal beams that do not rotate in the Larmor frame. For such beams, the theoretical predictions of the rms beam envelope, the conservations of the rms thermal emittances, the adiabatic equation of state, and the Debye length are verified in the simulations. Furthermore, the adiabatic thermal beam is found be stable in the parameter regime where the simulations are performed.United States. Dept. of Energy (Grant DEFG02- 95ER40919)United States. Dept. of Energy (Grant DE-FG02-05ER54836

Imprints of the Quantum World in Classical Mechanics

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.Comment: Paper submitted to Foundations of Physic

Families of Canonical Transformations by Hamilton-Jacobi-Poincar\'e equation. Application to Rotational and Orbital Motion

The Hamilton-Jacobi equation in the sense of Poincar\'e, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction. We illustrate our approach dealing with orbital and attitude dynamics. Based on the use of Whittaker and Andoyer symplectic charts, for which all but one coordinates are cyclic in the Hamilton-Jacobi equation, we provide whole families of canonical transformations, among which one recognizes the familiar ones used in orbital and attitude dynamics. In addition, new canonical transformations are demonstrated.Comment: 21 page

an inclusive view of saharan dust advections to italy and the central mediterranean

Abstract We address observations of physical and chemical properties of Saharan dust advections (SDA) as observed in the Central Mediterranean basin, within the framework of the LIFE+10, DIAPASON project ( www.diapason-life.eu ). DIAPASON aimed at the definition of best practices and tools to detect and evaluate the contribution of Saharan dust to ground particulate matter (PM) loads. Polarization-sensitive, automated lidar-ceilometers (PLC) are one of the tools prototyped and used in the Rome area to reach this goal. The results presented in this study focus on: 1) the effectiveness of various observational tools at detecting and characterizing atmospheric dust plumes, and 2) processes and properties of Saharan dust advections reaching the central Mediterranean region. In this respect, the combination of numerical model forecasts and time-resolved (at least hourly) PLC or chemical observations was found to constitute an efficient way to predict and confirm the presence of Saharan dust. In the period 2011–2014, Saharan dust advections were observed to reach over Rome on about 32% of the days. In some 70% of these days the dust reached the ground in dry conditions, while 30% of advection days involved wet deposition. Dry (wet) deposition was found to maximize (minimize) in summer. The northern Sahara between Algeria and Tunisia (Grand Erg Oriental), was confirmed as the most frequent region of origin of the dust mobilized towards central Italy. Secondary source regions include northern Morocco and Libya. On a statistical basis, Saharan advections to Rome were preceded by increasing atmospheric pressure and stability. These conditions were found to favor the accumulation of aerosols related to local emission sources before the SDA reached the ground. Meteorology (precipitation and turbulence in primis) resulted to be an important modulator of PM concentrations during SDAs. Magnitude and timing of these factors should be well considered to correctly evaluate the dust share in PM loads or the related health effects. Saharan advections observed during DIAPASON affected particle concentrations down to diameters of about 0.6–1 μm, with number concentrations peaking at the 2.5 μm diameter range. These advections were associated with a significant increase in Si-rich particles containing a non-negligible fraction of water. Rainfall was observed to preferentially remove dust particles larger than 2 μm, causing a significant depletion in the Ca-rich fraction with respect to the Si-rich one. The increase in PLC depolarization ratios above 5%, as well as the hourly PIXE records of the Si/Ca ratio increasing above 1 were found to represent good markers for the actual presence of Saharan dust particulate matter, when Saharan advection conditions are occurring

Heavy ion injector for the CERN Linac 1

An injector system has been designed to provide a fully stripped oxygen beam for acceleration in the CERN PS complex. An ECR source will provide an O/sup 6/+ beam to a heavy ion RFQ accelerator. The beam from the RFQ will be further accelerated by the CERN Linac 1 (Old Linac) in the 2 ..beta.. lambda-mode to an energy of 12.5 MeV/u at which point it will be fully stripped for subsequent acceleration in the CERN synchrotrons. The specifications of the new equipment and modifications to the existing linear accelerator are described