Non-dynamical Variables Research Articles

Canonical analysis of Holst action without second-class constraints

We perform the canonical analysis of the Holst action for general relativity with a cosmological constant without introducing second-class constraints. Our approach consists in identifying the dynamical and nondynamical parts of the involved variables from the very outset. After integrating out the nondynamical variables associated with the connection, we obtain the description of phase space in terms of manifestly $SO(3,1)$ [or $SO(4)$, depending on the signature] covariant canonical variables and first-class constraints only. We impose the time gauge on them and show that the Ashtekar-Barbero formulation of general relativity emerges. Later, we discuss a family of canonical transformations that allows us to construct new $SO(3,1)$ [or $SO(4)$] covariant canonical variables for the phase space of the theory and compare them with the ones already reported in the literature, pointing out the presence of a set of canonical variables not considered before. Finally, we resort to the time gauge again and find that the theory, when written in terms of the new canonical variables, either collapses to the $SO(3)$ ADM formalism or to the Ashtekar-Barbero formalism with a rescaled Immirzi parameter.

Canonical analysis ofn-dimensional Palatini action without second-class constraints

We carry out the canonical analysis of the $n$-dimensional Palatini action with or without a cosmological constant $(n\geq3)$ introducing neither second-class constraints nor resorting to any gauge fixing. This is accomplished by providing an expression for the spatial components of the connection that allows us to isolate the nondynamical variables present among them, which can later be eliminated from the action by using their own equation of motion. As a result, we obtain the description of the phase space of general relativity in terms of manifestly $SO(n-1,1)$ [or $SO(n)$] covariant variables subject to first-class constraints only, with no second-class constraints arising during the process. Afterwards, we perform, at the covariant level, a canonical transformation to a set of variables in terms of which the above constraints take a simpler form. Finally, we impose the time gauge and make contact with the $SO(n-1)$ ADM formalism.

Black hole perturbation in nondynamical and dynamical Chern-Simons gravity

Chern-Simons gravitational theories are extensions of general relativity in which the parity is violated due to the Chern-Simons term. We study linear perturbations on the static and spherically symmetric background spacetime both for nondynamical and dynamical Chern-Simons theories. We do not make an assumption that the background Chern-Simons scalar field vanishes, which has been adopted in the literature. By eliminating nondynamical variables using their constraint equations, we derive the reduced second order action from which a set of closed evolution equations containing only dynamical variables are immediately obtained and therefore the number of propagating degrees of freedom as well. It is found that ghost is present both for the nondynamical case and for the dynamical case unless the background Chern-Simons scalar field vanishes. It is also found that if the background scalar field vanishes, ghost degrees of freedom are killed and all the modes propagate at the speed of light.

CHAC: a weather pattern classification system for regional climate downscaling of daily precipitation

A weather pattern clustering method is applied and calibrated to Argentinean daily weather stations in order to predict daily precipitation data. The clustering technique is based on k-means and is applied to a set of 17 atmospheric variables from the ERA-40 reanalysis covering the period 1979–1999. The set of atmospheric variables represent the different components of the atmosphere (dynamical, thermal and moisture). Different sensitivity tests are applied to optimize (1) the number of observations (weather patterns) per cluster, (2) the spatial domain size of the weather pattern around the station and (3) the number of members of the ensembles. All the sensitivity tests are compared using the ROC (Relative Operating Characteristic) Skill Score (RSS) derived from the ROC curve used to assess the performance of a predictive system. First, we found the number of observations per cluster to be optimum for values larger than 39. Second, the spatial domain size (~4° × 4°) was found to be closer to a local scale than to a synoptic scale, certainly due to a dominant role of the moisture components in the optimization of the transfer function. Indeed, when reducing the set of variables to the subset of dynamical variables, the predictive skill of the method is significantly reduced, but at the same time the domain size must be increased. A potential improvement of the method may therefore be to consider different domains for dynamical and non-dynamical variables. Third, the number of members per ensembles of simulations was estimated to be always two to three times larger than the mean number of observations per cluster (meaning that at least all the observed weather patterns are selected by one member). The skill of the statistical method to predict daily precipitation is found to be relatively homogeneous all over the country for different thresholds of precipitation.

F-theory duals of M-theory onG2manifolds from mirror symmetry

Using mirror pairs (M3, W3) in type II superstring compactifications on Calabi–Yau threefolds, we study, geometrically, F-theory duals of M-theory on seven manifolds with G2 holonomy. We first develop a way of obtaining Landau–Ginzburg (LG) Calabi–Yau threefolds W3, embedded in four complex-dimensional toric varieties, mirror to the sigma model on toric Calabi–Yau threefolds M3. This method gives directly the right dimension without introducing non-dynamical variables. Then, using toric geometry tools, we discuss the duality between M-theory on S1 × M3/Z2 with G2 holonomy and F-theory on elliptically fibred Calabi–Yau fourfolds with SU(4) holonomy, containing W3 mirror manifolds. Illustrative examples are presented.

Characteristics Of Chaotic Attractors In Atmospheric Boundary-Layer Turbulence

In this paper, the attractors of turbulent flows in phase space are reconstructed by the time delay technique using observed data of atmospheric boundary-layer turbulence, which include high resolution temperature, humidity andthree-dimensional wind speed measurements in Gansu province and Beijing, China. The correlation dimensions and largest Lyapunov exponents have been computed. The results indicate that all the largest Lyapunov exponents in different conditions of time, site and atmospheric stability are greater than zero. This means that the atmospheric boundary-layer turbulence system is really chaotic and has appropriate low-dimensional strange attractors whose dimension numbers range from 3 to 7 and vary with different variables (dynamical variables or non-dynamical variables) and atmospheric stability. Turbulent kinetic energy is first applied to reconstruct the attractor of turbulence, and is found to be feasible.

Nonlocal Electrodynamics in 2+1 Dimensions from Chern–Simons Theory**The project supported by Doctoral Program Foundation of the National Education Commission of China, and by National Natural Science Foundation of China

The theory of a spinor field interacting with a pure Chern–Sirnons gauge field in 2+1 dimensions is quantized. Dynamical and nondynamical variables are separated in a gaugeindependent way. After the nondynamical variables are dropped, this theory reduces to a pure spinor field theory with nonlocal interaction. Several two-body scattering processes are studied and the crbss sections are obtained in explicitly Lorentz-invariant forms.

Nonlocal Scalar Electrodynamics from Chern-Simons Theory**The project supported by the Doctoral Foundation of the National Education Commission of China

The theory of a complex scalar interacting with a pure Chern–Simons gauge field is quantized canonically. Dynamical and nondynamical variables are separated in a gauge-independent way. In the physical subspace of the full Hilbert space, this theory reduces to a pure scalar theory with nonlocal interaction. Several scattering processes are studied and the cross sections are calculated.

Gauge fixing and independent canonical variables in the Ashtekar formulation of general relativity

We analyse gauge fixing and the corresponding reduced phase space for the Ashtekar formulation of general relativity. In the gauge where the local frame rotations are fixed by setting to zero three components of the complex connection, and the space-time diffeomorhpisms are fixed by setting three components of the triads to zero and one component to be the time, we find an explicit expression for the hamiltonian of the independent canonical variables. Although non-local, it is quadratic in the physical variables, which raises the possibility of solving completely the corresponding Schrödinger equation. Unfortunately, we could not solve all of the constraint equations for the non-dynamical variables, so that the construction of the physical variables is obstructed.

Hamiltonian Structure of Poincaré Gauge Theory and Separation of Non-Dynamical Variables in Exact Torsion Solutions

The canonical Hamiltonian of the Poincaré gauge theory of gravity is reanalyzed for generic Lagrangians. It is shown that the time components e0α and Γ0αβ of the tetrad and the linear connection fields of a Riemann-Cartan space-time U4 constitute gauge degrees of freedom which remain non-dynamical during the time evolution of the system. Whereas the e0α are to be identified with the lapse and shift functions Nα known from the ADM formalism in Einstein's theory, the additional Lorentz degrces of freedom Γ0αβ are pertinent to Poincaré gauge models. These non-dynamical variables are instrumental in the derivation of exact torsion solutions obeying modified double duality conditions for the U4-curvature. Thereby, in the case of spherical symmetry and for the charged Taub-NUT metric, we obtain the most general torsion configuration for a large class of quadratic Lagrangians. Previously found solutions are contained therein and can be recovered after fixing special “gauge”.