Low-energy sector of 8-dimensional General Relativity: Electro-Weak model and neutrino mass

In a Kaluza-Klein space-time $V^{4}\otimes S^{3}$, we demonstrate that the dimensional reduction of spinors provides a 4-field, whose associated SU(2) gauge connections are geometrized. However, additional and gauge-violating terms arise, but they are highly suppressed by a factor $\beta$, which fixes the amount of the spinor dependence on extra-coordinates. The application of this framework to the Electro-Weak model is performed, thus giving a lower bound for $\beta$ from the request of the electric charge conservation. Moreover, we emphasize that also the Higgs sector can be reproduced, but neutrino masses are predicted and the fine-tuning on the Higgs parameters can be explained, too.Comment: 14 pages, 1 figure, to appear on Int. J. Mod. Phys.

Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model

We study the Gross-Neveu model in $2+1$ dimensions in an external magnetic field $B$. We first summarize known mean-field results, obtained in the limit of large flavor number $N_\mathrm{f}$, before presenting lattice results using the overlap discretization to study one reducible fermion flavor, $N_\mathrm{f}=1$. Our findings indicate that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, persists beyond the mean-field limit for temperatures below the chiral phase transition and that the critical temperature grows with increasing magnetic field. This is in contrast to the situation in QCD, where the broken phase shrinks with increasing $B$ while the condensate exhibits a non-monotonic $B$-dependence close to the chiral crossover, and we comment on this discrepancy. We do not find any trace of inhomogeneous phases induced by the magnetic field.Comment: 10 pages + 4 pages appendix, 10 figure

Fermion Dynamics by Internal and Space-Time Symmetries

This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat space-time and the role of the torsion field, within the generalization to curved space-time, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.Comment: 10 pages, no figur

A description of the f2(1270), rho3(1690), f4(2050), rho5(2350) and f6(2510) resonances as multi-rho(770) states

In a previous work regarding the interaction of two $\rho(770)$ resonances, the $f_2(1270)$ ($J^{PC}=2^{++}$) resonance was obtained dynamically as a two-$\rho$ molecule with a very strong binding energy, 135~MeV per $\rho$ particle. In the present work we use the $\rho\rho$ interaction in spin 2 and isospin 0 channel to show that the resonances $\rho_3(1690)$ ($3^{--}$), $f_4(2050)$ ($4^{++}$), $\rho_5(2350)$ ($5^{--}$) and $f_6(2510)$ ($6^{++}$) are basically molecules of increasing number of $\rho(770)$ particles. We use the fixed center approximation of the Faddeev equations to write the multi-body interaction in terms of the two-body scattering amplitudes. We find the masses of the states very close to the experimental values and we get an increasing value of the binding energy per $\rho$ as the number of $\rho$ mesons is increased.Comment: 17 pages, 6 figure

Decay of accelerated particles

We study how the decay properties of particles are changed by acceleration. It is shown that under the influence of acceleration (1) the lifetime of particles is modified and (2) new processes (like the decay of the proton) become possible. This is illustrated by considering scalar models for the decay of muons, pions, and protons. We discuss the close conceptual relation between these processes and the Unruh effect.Comment: Latex2e, 12 pages, 6 Postscript figures included with epsfig, to appear in Phys. Rev.

Generating functional for the gravitational field: implementation of an evolutionary quantum dynamics

We provide a generating functional for the gravitational field, associated to the relaxation of the primary constraints as extended to the quantum sector. This requirement of the theory, relies on the assumption that a suitable time variable exist, when taking the T-products of the dynamical variables. More precisely, we start from the gravitational field equations written in the Hamiltonian formalism and expressed via Misner-like variables; hence we construct the equation to which the T-products of the dynamical variables obey and transform this paradigm in terms of the generating functional, as taken on the theory phase-space. We show how the relaxation of the primary constraints (which correspond to break down the invariance of the quantum theory under the 4-diffeomorphisms) is summarized by a free functional taken on the Lagrangian multipliers, accounting for such constraints in the classical theory. The issue of our analysis is equivalent to a Gupta-Bleuler approach on the quantum implementation of all the gravitational constraints; in fact, in the limit of small $\hbar$, the quantum dynamics is described by a Schr\"odinger equation, as soon as the mean values of the momenta, associated to the lapse function and the shift vector, are not vanishing. Finally we show how, in the classical limit, the evolutionary quantum gravity reduces to General Relativity in the presence of an Eckart fluid, which corresponds to the classical counterpart of the physical clock, introduced in the quantum theory.Comment: 23 pages, no figures, to appear on International Journal of Modern Physics

Two-electron atoms, ions and molecules

The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$, cannot be achieved using a mere product of individual electron wave functions, and requires instead an explicit account for the anticorrelation among the two electrons. The wave function proposed by Chandrasekhar is revisited, where the permutation symmetry is first broken and then restored by a counter-term. More delicate problems can be studied using the same strategy: the stability of hydrogen-like ions $(M^+,m^-,m^-)$ for any value of the proton-to-electron mass ratio $M/m$; the energy of the lowest spin-triplet state of helium and helium-like ions; the stability of the doubly-excited hydrogen ion with unnatural parity. The positronium molecule $(e^+,e^+,e^-,e^-)$, which has been predicted years ago and discovered recently, can also be shown to be stable against spontaneous dissociation, though the calculation is a little more involved. Emphasis is put on symmetry breaking which can either spoil or improve the stability of systems.Comment: 16 pages, 2 figure

Non-Markovian entanglement dynamics of quantum continuous variable systems in thermal environments

We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of electromagnetic fields or two nanomechanical oscillators in the quantum domain. We use quantum open system method to derive the non-Markovian master equations of the reduced density matrix for two different but related models of the continuous variable systems. The two models both consist of two interacting harmonic oscillators. In model A, each of the two oscillators is coupled to its own independent thermal reservoir, while in model B the two oscillators are coupled to a common reservoir. To quantify the degrees of entanglement for the bipartite continuous variable systems in Gaussian states, logarithmic negativity is used. We find that the dynamics of the quantum entanglement is sensitive to the initial states, the oscillator-oscillator interaction, the oscillator-environment interaction and the coupling to a common bath or to different, independent baths.Comment: 10 two-column pages, 8 figures, to appear in Phys. Rev.

The “central state” and the almighty Dollar

New methods to determine the titanium (Ti) mass-dependent isotope fractionation of solar system materials to high precision were developed by combining internally normalised Ti isotope data with double-spike analyses utilising a 47Ti-49Ti double spike. The procedure includes a three-stage ion-exchange separation procedure to isolate Ti from the sample matrix that provides high-purity Ti fractions that are necessary for high-precision Ti isotope analyses. Analyses of sample aliquots that were spiked before and after the ion-exchange separation procedure demonstrate that Ti isotope fractionation can be induced by the separation procedure. This outcome requires the addition of the double spike before the ion exchange separation procedure in order to accurately determine the natural mass-dependent Ti isotope fractionation of samples. Multiple double spike analyses of an Alfa Aesar Ti standard performed over eight months yielded a reproducibility (2σ standard deviation) of 0.033‰ for δ49/47Ti (differences in 49Ti/47Ti relative to the OL-Ti standard). Terrestrial sample analyses display a 2σ reproducibility of 0.018 to 0.031‰ for δ49/47Ti. Titanium isotope results for three terrestrial USGS magmatic reference samples (AGV-2, BHVO-2 and BCR-2) agree well with literature data and therefore demonstrate the accuracy and precision of the presented methodologies. Achondritic meteorites display an overall range of 0.75‰ for δ49/47Ti. The ungrouped achondrite NWA 7325 has a more positive composition by 0.64‰ for δ49/47Ti compared to all other investigated samples likely reflecting Ti isotope fractionation induced by magmatic differentiation associated with highly reducing conditions and potentially associated with oxide and plagioclase formation. In contrast, eucrites with δ49/47Ti of -0.020 ± 0.070 and -0.003 ± 0.033 and the first mass-dependent Ti isotope data for an acapulcoite (Dhofar 125; δ49/47Ti = 0.094 ± 0.033) show only limited magmatic Ti isotope fractionation. Chondrites also display a relatively restricted range of 0.085‰ for δ49/47Ti, including one calcium‑aluminum rich inclusion (CAI) from Allende and the first mass-dependent Ti isotope data for two Rumuruti chondrites (NWA 753 and NWA 755). Furthermore, the mass-dependent Ti isotope composition of chondrites overlaps with that of eucrites and the acapulcoite Dhofar 125 indicating that nebular processes induce only limited Ti isotope fractionation. Additionally, the Ti isotope data indicate that thermal metamorphism also produced marginal Ti isotope fractionation at the bulk sample scale for chondrites. Small mass-dependent Ti isotope variations between different bulk meteorite samples are also evident, which might reflect sample heterogeneity. Importantly, the mass-dependent Ti isotope composition of the Earth and Moon overlap with the composition of the investigated chondrites, eucrites and acapulcoites within the 2 standard deviation uncertainties