New Variables Research Articles

Abelian Ashtekar formulation from the ADM action

We study the Ashtekar formulation of linear gravity starting from the Arnowitt–Deser–Misner (ADM) first-order action of the exact theory, linearizing it, and performing a canonical transformation that coordinatizes the phase-space in terms of the already linearized Ashtekar variables. A quantum geometrical representation, based on the realization of the transverse-traceless part of the linear canonical variables, is presented, and its relationship with previous attempts is discussed. A related geometric representation that realizes directly the observables of the Fierz–Pauli theory, without resorting to deal with the linearized Ashtekar variables, is also discussed.

Influence of mediating/moderating effects of health skills on the relation between knowledge and behaviors in health, among college students

To study the influence of mediating/moderating effects of health skills on the relations between health knowledge and health behaviors in college students. Stratified cluster random sampling was used among 2 181 students, selected in several colleges in Changsha, Hunan province. EpiData 3.0 was adopted to establish the database. Correlation and regression analyses were performed by SPSS 17.0. Positive correlations were seen on: 1) Knowledge and skills on health (r = 0.592, P < 0.01), 2) Knowledge and behaviors on health (r = 0.647, P < 0.01), 3) Health skills and health behaviors(r = 0.629, P < 0.01). The mediating effect of health skills on the relations between health knowledge and health behaviors was significant (34.55%). The interaction effect of "health skill × (times) related knowledge" was significant (β = -0.093, t = - 5.212, P = 0.000). New variables that were produced by the interaction also reached significant level (Δ R(2) = 0.006, P = 0.000), resulted in increasing the explanation function to health behaviors by 0.6%. Health skills could partially mediate the effects and moderate the relationship between health knowledge and health behaviors among college students.

Adopting Lanchester Model to the Ardennes Campaign with Deadlock Situation in the Shift Time between Defense and Attack

General Karl Von Clausewitz believes that attack and defense in warfare are a state of interaction and response. The shift between attack and defense is involved with a short span of time difficult to define in concrete format. This paper extends Chen and Chu's model of the Ardennes campaign of World War II using the Lanchester equations. We use a new variable, deadlocked situation, to represent the shifting time between attack and defense. This article divides the Ardennes Campaign into three periods: (a) the initial period, German attacked while the Allies defended; (b) the middle period, both sides seized the initiative; (c) the final period, Allies attacked while Germans defended. In this paper, we apply Lanchester's Square Law to estimate the casualties by determining the shifting time between attack and defense. We obtain improved goodness of fit for the historical data.

Reformulation of the Hamiltonian constraint of four-dimensional gravity for arbitrary values of the Immirzi parameter via the affine group formalism

One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to implement reality conditions in the Lorentzian signature case. A reformulation of the theory in terms of real variables eliminates this difficulty, albeit at the expense of having to deal with a more complicated Hamiltonian constraint. The set of available gravitational theories classically equivalent to Einstein’s is parametrized by a parameter β, known as the Immirzi parameter. We rephrase the Hamiltonian constraint into the form of an affine Lie algebra for arbitrary β, and perform a quantization.

C*-algebras of holonomy-diffeomorphisms and quantum gravity: I

A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a quantized Dirac-type operator, the two capturing the kinematics of quantum gravity formulated in terms of Ashtekar variables. We prove that the separable part of the spectrum of the algebra is contained in the space of measurable connections modulo gauge transformations and we give limitations to the non-separable part. The construction of the Dirac-type operator—and thus the application of noncommutative geometry—is motivated by the requirement of diffeomorphism invariance. We conjecture that a semi-finite spectral triple, which is invariant under volume-preserving diffeomorphisms, arises from a GNS construction of a semi-classical state. Key elements of quantum field theory emerge from the construction in a semi-classical limit, as does an almost commutative algebra. Finally, we note that the spectrum of loop quantum gravity emerges from a discretization of our construction. Certain convergence issues are left unresolved. This paper is the first of two where the second paper [1] is concerned with mathematical details and proofs concerning the spectrum of the holonomy-diffeomorphism algebra.

A new ultrasonic exponential decay pulser technique for low concentrations detection and measurements

The objective of this study was to design and implement a new ultrasonic pulser with adjustable concentration detection. The new technique based on transmits a multiple ultrasound pulses with decay power through slurry to determine the lowest concentration that can provide an accurate attenuation measurement and wide measurement range. The ultrasonic pulser was designed to transmit a reliable pulsed-power decay set that can be reprogrammed with new output variables, e.g. ,the pulse amplitude, the pulse frequency, the set size, the decay power factor of the pulse amplitude, the transmit mode, and the time interval. Ultrasound attenuation measurements were obtain for kaolin-water slurries with1%, 10%, 20%, 30%, and 40% kaolin concentration by weight. Concentration attenuation measurements of less than 5% may prove useful for process control when detecting contaminants. A long measurement level is obtained from the pulsed-power transmission, regardless of the material used to construct the container. A signal in the receiver transducer provides the attenuation measurements, for each echo, a fast Fourier transform (FFT) of the appropriate signal was obtained and compared with the water signals to yield the attenuation (as a function of frequency). The data show the feasibility of measuring a kaolin concentration of less than 5 wt%. When using a commercial pulser with the same device setting, no detectable echo was observed. Therefore, new technique measurements may prove useful in detecting solid content in liquid. This study demonstrated that the proposed pulsed-power transmission technique is promising for evaluating low concentrations of solids in fluids and for measuring sedimentation in solid-liquid systems.

Affine group representation formalism for four-dimensional, Lorentzian, quantum gravity

Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure general relativity with cosmological constant, Λ, is re-expressed as an affine algebra with the commutator of the imaginary part of the Chern–Simons functional, Q, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant, and it facilitates the construction of solutions to all of the constraints. Unitary, irreducible representations of the affine group exhibit a natural Hilbert space structure, and coherent states and other physical states can be generated from a fiducial state. It is also intriguing that formulation of the Hamiltonian constraint or the Wheeler–DeWitt equation as an affine algebra requires a non-vanishing cosmological constant, and a fundamental uncertainty relation of the form (wherein V is the total volume) may apply to all physical states of quantum gravity.

A Novel Planar Transformer Design Based on a Variable Width Winding

The trend toward high power density, high operating frequency and low profile packaging in power converters will determine designers to replace the conventional Cu-wires transformers with planar transformers. In this paper a novel variable track width per turn design is proposed for the transformer windings. The basic design idea consists of matching the winding resistances per turn in order to maintain a flux balance among turns. The complete design methodologies for both variable and constant width windings are presented and compared. Theoretical design equations are confirmed using a finite element analysis (FEA) simulation. A 10W half bridge LLC converter prototype has been constructed employing both winding structures. Experimental results show a 0.4% converter efficiency improvement using the novel planar transformer based on the new variable width design compared to the conventional constant width approach

A New Solar Reactor Aperture Mechanism Coupled with Heat Exchanger

Concentrated solar energy finds applications for power generation and as a source of heat for solar thermochemical processes. However, solar energy reaching the earth’s surface is intermittent and fluctuates with weather conditions, position of the sun throughout the day and other seasonal changes. This causes a major drawback in receiver efficiency as semi-constant temperatures are required for efficient operation of solar thermochemical processes. This paper introduces a new variable aperture mechanism which is coupled with a heat exchanger to collect unused heat during peak times. The paper presents an optical and heat transfer analysis of the concept using Monte-Carlo ray tracing technique via TracePro and an in-house developed heat transfer code. The heat transfer analysis of the proposed concept shows the optimum aperture diameter with a compromise between reactor temperature and reradiation losses. It also predicts the losses incurred by the variable sized aperture mechanism when the incoming solar radiation changes.

Hořava-Lifshitz theory as a fermionic aether in Ashtekar gravity

We show how Ho\v{r}ava-Lifshitz (HL) theory appears naturally in the Ashtekar formulation of relativity if one postulates the existence of a fermionic field playing the role of aether. The spatial currents associated with this field must be switched off for the equivalence to work. Therefore the field supplies the preferred frame associated with breaking refoliation (time diffeomorphism) invariance, but obviously the symmetry is only spontaneously broken if the field is dynamic. When Dirac fermions couple to the gravitational field via the Ashtekar variables, the low energy limit of HL gravity, recast in the language of Ashtekar variables, naturally emerges (provided the spatial fermion current identically vanishes). HL gravity can therefore be interpreted as a time-like current, or a Fermi aether, that fills space-time, with the Immirzi parameter, a chiral fermionic coupling, and the fermionic charge density fixing the value of the parameter $\lambda$ determining HL theory. This reinterpretation sheds light on some features of HL theory, namely its good convergence properties.

Linking covariant and canonical general relativity via local observers

Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables. The key is viewing dynamical fields from the perspective of a field of observers -- a unit timelike vector field that also transforms under local Lorentz transformations. On one hand, all fields are spacetime fields, covariant under spacetime symmeties. On the other, when the observer field is normal to a spatial foliation, the fields automatically fall into Hamiltonian form, recovering the Ashtekar formulation. We argue this provides a bridge between Ashtekar variables and covariant phase space methods. We also outline a framework where the 'space of observers' is fundamental, and spacetime geometry itself may be observer-dependent.

On Ashtekar's Formulation of General Relativity

We review Ashtekar's variables in physics and in mathematics notation. The first one uses local indices, the second one is given by global objects within fibre bundles.

Plane Gravitational Waves and Loop Quantization

Starting from the polarized Gowdy model in Ashtekar variables, the Killing equations characteristic for plane-fronted parallel gravitational waves are introduced in part as a set of first-class constraints, in addition to the standard ones of General Relativity. These constraints are expressed in terms of quantities that have an operator equivalent in Loop Quantum Gravity, making plane wave space-times accessible to loop quantization techniques.

Chiral vacuum fluctuations in quantum gravity

In this paper we investigate cosmological tensor modes in terms of the Ashtekar variables of loop quantum gravity, for complex values of the Immirzi parameter. While, on-shell, the classical Hamiltonian reduces to the usual expression found in cosmological perturbation theory, the quantum Hamiltonian displays significant differences. We can find a physical Fourier space Hamiltonian in terms of graviton creation and annihilation operators, after selecting out the non-physical modes through the inner product which itself is determined by the reality conditions. We are left with the usual graviton modes but with a chiral asymmetry in the the vacuum energy and fluctuations. The latter depends on γ (in particular it vanishes for purely real γ) and on the ordering of the 2-point function. Such an effect would leave a distinctive imprint in the polarisation of the cosmic microwave background, thus finally engaging quantum gravity in meaningful experimental test.

Boundary Terms and the 3 + 1 Decomposition of the Holst Action

Starting from the Holst action with surface terms and the fall-off conditions that make the variational principle and the covariant phase space formulation well-defined for asymptotically flat spacetimes, we rewrite the surface terms in the 3+1 decomposition of the action. We explore their relation with the surface terms in the Hamiltonian formulation in terms of Ashtekar variables. Just as for the Einstein-Hilbert action, if variations respecting asymptotic flatness are allowed, the energy and momentum in the Hamiltonian framework are not directly recovered from the 3+1 decomposition and gauge fixing of these terms.

Barbero–Immirzi parameter, manifold invariants and Euclidean path integrals

The Barbero–Immirzi parameter γ appears in the real connection formulation of gravity in terms of the Ashtekar variables, and gives rise to a one-parameter quantization ambiguity in loop quantum gravity. In this paper, we investigate the conditions under which γ will have physical effects in Euclidean quantum gravity. This is done by constructing a well-defined Euclidean path integral for the Holst action with a non-zero cosmological constant on a manifold with a boundary. We find that two general conditions must be satisfied by the spacetime manifold in order for the Holst action and its surface integral to be non-zero: (i) the metric has to be non-diagonalizable; (ii) the Pontryagin number of the manifold has to be non-zero. The latter is a strong topological condition and rules out many of the known solutions to the Einstein field equations. This result leads us to evaluate the on-shell first-order Holst action and corresponding Euclidean partition function on the Taub–NUT–ADS solution. We find that γ shows up as a finite rotation of the on-shell partition function which corresponds to shifts in the energy and entropy of the NUT charge. In an appendix, we also evaluate the Holst action on the Taub–NUT and Taub–bolt solutions in flat spacetime and find that in that case as well γ shows up in the energy and entropy of the NUT and bolt charges. We also present an example whereby the Euler characteristic of the manifold has a non-trivial effect on black hole mergers.Communicated by PRLV Moniz

Local Hamiltonian for spherically symmetric collapse: Geometrodynamics approach

Recently, a local true (completely gauge fixed) Hamiltonian for spherically symmetric collapse was derived in terms of Ashtekar variables. We show that such a local Hamiltonian follows directly from the geometrodynamics of gravity theories that obey a Birkhoff theorem and possess a mass function that is constant on the constraint surface in vacuum. In addition to clarifying the geometrical content, our approach has the advantage that it can be directly applied to a large class of spherically symmetric and two-dimensional gravity theories, including $p$th order Lovelock gravity in $D$ dimensions. The resulting expression for the true local Hamiltonian is universal and remarkably simple in form.

Speaking Stata: Output to Order

Wanting to present Stata output in a different way is a very common desire that lies behind many substantial user-written programs. Here I start at the beginning with some basic tips and tricks. I discuss using display to replay the results you want; putting results into new variables so that they can be listed, tabulated, or plotted; and using existing reduction commands to produce new datasets containing results.

Chirality of tensor perturbations for complex values of the Immirzi parameter

In this communication, we generalize previous work on tensor perturbations in a de Sitter background in terms of Ashtekar variables to cover all complex values of the Immirzi parameter γ (previous work was restricted to imaginary γ). Particular attention is paid to the case of real γ. Following the same approach as in the imaginary case, we can obtain physical graviton states by invoking reality and torsion-free conditions. The Hamiltonian in terms of graviton states has the same form whether γ has a real part or not; however, changes occur for the vacuum energy and fluctuations. Specifically, we observe a γ-dependent chiral asymmetry in the vacuum fluctuations only if γ has an imaginary part. Ordering prescriptions also change this asymmetry. We thus present a measurable result for CMB polarization experiments that could shed light on the workings of quantum gravity.

Twistorial phase space for complex Ashtekar variables

We generalize the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group . We show that the phase space for complex-valued Ashtekar variables on a spin-network graph can be decomposed in terms of twistorial variables. To every link there are two twistors—one to each boundary point—attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered.