Orchidea Maria Lecian

Spacetime-noncommutativity regime of loop quantum gravity

A recent study by Bojowald and Paily [M. Bojowald and G. M. Paily, Phys. Rev. D 87, 044044 (2013).PRVDAQ1550-799810.1103/PhysRevD.87.044044] provided a path toward the identification of an effective quantum-spacetime picture of loop quantum gravity, applicable in the “Minkowski regime,” the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by loop-quantum-gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the κ-Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.

Implications of non-analytical f(R) gravity at Solar-System scales

We motivate and analyze the weak-field limit of a non-analytic modification of the Einstein–Hilbert Lagrangian for the gravitational field. After investigating the parameter space of the model, we impose constraints on the parameters characterizing this class of theories by means of solar system data, i.e. we establish the validity range where this solution applies and refine the constraints by comparison with planetary orbits. As a result, we claim that this class of models is viable within different astrophysical scales.

Canonical quantum gravity : fundamentals and recent developments

General Relativity Quantization Methods Classical and Quantum Geometrodynamics Gravity as a Gauge Theory Loop Quantum Gravity Quantum Cosmology.

FERMION DYNAMICS BY INTERNAL AND SPACETIME SYMMETRIES

This paper is devoted to introduce a gauge theory of the Lorentz group based on the ambiguity emerging in dealing with isometric diffeomorphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat spacetime and the role of the torsion field, within the generalization to curved spacetime, 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.

Polymer quantum dynamics of the Taub universe

Within the framework of nonstandard (Weyl) representations of the canonical commutation relations, we investigate the polymer quantization of the Taub cosmological model. The Taub model is analyzed within the Arnowitt-Deser-Misner reduction of its dynamics, by which a time variable arises. While the energy variable and its conjugate momentum are treated as ordinary Heisenberg operators, the anisotropy variable and its conjugate momentum are represented by the polymer technique. The model is analyzed at both classical and quantum level. As a result, classical trajectories flatten with respect to the potential wall, and the cosmological singularity is not probabilistically removed. In fact, the dynamics of the wave packets is characterized by an interference phenomenon, which, however, is not able to stop the evolution towards the classical singularity.

LORENTZ GAUGE THEORY AND SPINOR INTERACTION

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.

ABOUT THE STATISTICAL PROPERTIES OF COSMOLOGICAL BILLIARDS

We summarize some recent progress in the understanding of the statistical properties of cosmological billiards.

Semiclassical and quantum behavior of the mixmaster model in the polymer approach

We analyze the quantum dynamics of the Bianchi Type IX model, as described in the so-called polymer representation of quantum mechanics, to characterize the modifications that a discrete nature in the anisotropy variables of the Universe induces on the morphology of the cosmological singularity. We first perform a semiclassical analysis, to be regarded as the zeroth-order approximation of a WKB approximation of the quantum dynamics, and demonstrate how the features of polymer quantum mechanics are able to remove the chaotic properties of the Bianchi IX dynamics. The resulting evolution towards the cosmological singularity overlaps the one induced, in a standard Einsteinian dynamics, by the presence of a free scalar field. Then, we address the study of the full quantum dynamics of this model in the polymer representation and analyze the two cases in which the Bianchi IX spatial curvature does not affect the wave-packet behavior, as well as the instance for which it plays the role of an infinite potential confining the dynamics of the anisotropic variables. The main development of this analysis consists of investigating how, differently from the standard canonical quantum evolution, the high quantum number states are not preserved arbitrarily close to the cosmological singularity. This property emerges as a consequence, on one hand, of the no-longer-chaotic features of the classical dynamics (on which the Misner analysis is grounded), and, on the other hand, of the impossibility of removing the quantum effect due to the spatial curvature. In the polymer picture, the quantum evolution of the Bianchi IX model remains always significantly far from the semiclassical behavior, as far as both the wave-packet spread and the occupation quantum numbers are concerned. As a result, from a quantum point of view, the mixmaster dynamics loses any predictivity characterization for the discrete nature of the Universes anisotropy.

Stueckelberg: A Forerunner of modern physics. II.

We will investigate some aspects of Stueckelbergs work, which have contributed to the development of modern physics. On the one hand, the definition of diffuse boundaries in the calculation of scattering amplitudes will be reviewed, and compared with the other proposals by physicists of that time. On the other hand, the applications of Stueckelbergs description of a massive vector field in the Standard Model will be discussed.

EXPONENTIAL LAGRANGIAN FOR THE GRAVITATIONAL FIELD AND THE PROBLEM OF VACUUM ENERGY

We will analyze two particular features of an exponential gravitational Lagrangian. On the one hand, while this choice of the Lagrangian density allows for two free parameters, only one scale, the cosmological constant, arises as fundamental when the proper Einsteinian limit is to be recovered. On the other hand, the vacuum energy arising from f(R) theories such that f(0) ≠ 0 needs a cancellation mechanism, by which the present value of the cosmological constant can be recast.