Solving the Constraints of General Relativity

I show in this letter that it is possible to solve some of the constraints of the $SO(3)$-ADM formalism for general relativity by using an approach similar to the one introduced by Capovilla, Dell and Jacobson to solve the vector and scalar constraints in the Ashtekar variables framework. I discuss the advantages of using the ADM formalism and compare the result with similar proposals for different Hamiltonian formulations of general relativity.Comment: 8 pages, LATEX, no figures, Preprint CGPG-94/11-

Weak Magnetism in Two Neutrino Double Beta Decay

We have extended the formalism for the two-neutrino double beta decay by including the weak-magnetism term, as well as other second-forbidden corrections. The weak magnetism diminishes the calculated half-lives in $\sim 10$, independently of the nuclear structure. Numerical computations were performed within the pn-QRPA, for $^{76}Ge$, $^{82}Se$, $^{100} Mo$, $^{128}Te$ and $^{130}Te$ nuclei. No one of the second-forbidden corrections modifies significantly the spectrum shapes. The total reduction in the calculated half lives varies from 6% up to 32%, and strongly depend on the nuclear interaction in the particle-particle $S=1,T=0$ channel. We conclude that the higher order effects in the weak Hamiltonian would hardly be observed in the two-neutrino double beta experiments.Comment: 8 pages, latex, 1ps figure, to appear in Phys. Lett.

Competition between standard and exotic double beta decays

We discuss the contributions of higher order terms in weak Hamiltonian to the standard two-neutrino double beta decay. The formalism for the unique first forbidden transitions has been developed, and it is shown that they can alter the two-electron energy spectrum. Yet, their effect is too small to screen the detection of exotic neutrinoless double beta decays, which are candidates for testing the physics beyond the standard model.Comment: 9 pages, latex, 1ps figures, minor changes, to appear in Phys. Lett.

SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter

An so(4,C)-covariant hamiltonian formulation of a family of generalized Hilbert-Palatini actions depending on a parameter (the so called Immirzi parameter) is developed. It encompasses the Ashtekar-Barbero gravity which serves as a basis of quantum loop gravity. Dirac quantization of this system is constructed. Next we study dependence of the quantum system on the Immirzi parameter. The path integral quantization shows no dependence on it. A way to modify the loop approach in the accordance with the formalism developed here is briefly outlined.Comment: 14 pages, LATEX; minor changes; misprints corrected; commutator of two secondary second class constraints correcte

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.

Nonmesonic weak decay spectra of Λ4^4_\LambdaHe

To comprehend the recent Brookhaven National Laboratory experiment E788 on $^4_\Lambda$He, we have outlined a simple theoretical framework, based on the independent-particle shell model, for the one-nucleon-induced nonmesonic weak decay spectra. Basically, the shapes of all the spectra are tailored by the kinematics of the corresponding phase space, depending very weakly on the dynamics, which is gauged here by the one-meson-exchange-potential. In spite of the straightforwardness of the approach a good agreement with data is acheived. This might be an indication that the final-state-interactions and the two-nucleon induced processes are not very important in the decay of this hypernucleus. We have also found that the $\pi+K$ exchange potential with soft vertex-form-factor cutoffs $(\Lambda_\pi \approx 0.7$ GeV, $\Lambda_K \approx 0.9$ GeV), is able to account simultaneously for the available experimental data related to $\Gamma_p$ and $\Gamma_n$ for $^4_\Lambda$H, $^4_\Lambda$He, and $^5_\Lambda$He.Comment: 12 pages, 4 figures, 1 table, submitted for publication; v2: major revision, 18 pages, one author added, table, figures and bibliography change

Real Ashtekar Variables for Lorentzian Signature Space-times

I suggest in this letter a new strategy to attack the problem of the reality conditions in the Ashtekar approach to classical and quantum general relativity. By writing a modified Hamiltonian constraint in the usual $SO(3)$ Yang-Mills phase space I show that it is possible to describe space-times with Lorentzian signature without the introduction of complex variables. All the features of the Ashtekar formalism related to the geometrical nature of the new variables are retained; in particular, it is still possible, in principle, to use the loop variables approach in the passage to the quantum theory. The key issue in the new formulation is how to deal with the more complicated Hamiltonian constraint that must be used in order to avoid the introduction of complex fields.Comment: 10 pages, LATEX, Preprint CGPG-94/10-

On the propagation speed of evanescent modes

The group-velocity of evanescent waves (in undersized waveguides, for instance) was theoretically predicted, and has been experimentally verified, to be Superluminal (v_g > c). By contrast, it is known that the precursor speed in vacuum cannot be larger than c. In this paper, by computer simulations based on Maxwell equations only, we show the existence of both phenomena. In other words, we verify the actual possibility of Superluminal group velocities, without violating the so-called (naive) Einstein causality. (Subject classes: General physics, Classical physics, Optics, Special Relativity; PACS nos.: 73.40Gk, 03.80+z, 03.65Bz; Keywords: evanescent waves; tunnelling photons; Hartman effect; group velocity; Superluminal waves; precursors; transient waves; front velocity; Maxwell equations; electromagnetic waves; computer simulations; Special Relativity; Extended Relativity).Comment: plain LaTeX file (14 pages), plus 15 figures in .jp