- XI Marcel Grossmann Meeting (Berlin, June 2006)

 

Abstract:

Evolutionary Reformulation of the Quantum Gravity
Author: Giovanni Montani
Speaker: Giovanni Montani

We present a critical analysis of the Canonical approach to quantum Gravity, which relies on the ambiguity of implementing a space-time slicing on the quantum level. We emphasize that such a splitting procedure is consistent only if a real matter fluid is involved in the dynamics, because it is endowed by a time-like versor. Since the non-test character of a quantum reference frame is fixed, then a dualism between a dust fluid and a physical time variable arises. The phenomenological issues of a Schr¨odinger quantum gravity are then discussed and the overlap to the Wheeler-DeWitt approach is established.

 

 

Electro-WeakModel within a 5-dimensional Lorentz group theory
Authors: Orchidea Maria Lecian, Giovanni Montani
Speaker: Orchidea Maria Lecian

The Electro-Weak Model is geometrized in a Riemann-Cartan space, within a 5-dimensional Kaluza-Klein scenario. A natural chirality is shown by the 5- dimensional extension of spinorial fields. U (1) weak hyper-charge gauge fields come from the off-diagonal components of the 5-dimensional metric tensor, while SU (2) weak isospin gauge fields are identified in the bein projection of the extradimensional components of the contortion field (the Lorentz gauge vectors). In the framework of a gauge theory of the Lorentz group, conserved gauge charges are recognized in the bein projection of the spin part of the angular momentum tensor in 4 dimensions, whereas, in 5 dimensions, the pertinent conserved current allows us to fix the proper SU (2) generators. Under these two geometrized symmetries, spinorial fields meet the proper transformation laws. The possibility of extending Ashtekar formalism to 5-dimensional Kaluza-Klein theories is investigated.

 

 

The electro-weak model as a phenomenological limit of a Kaluza-Klein theory.
Authors: Francesco Cianfrani, Giovanni Montani
Speaker: Francesco Cianfrani

We consider Kaluza-Klein theories as candidates for the unification of gravity and other interactions. In particular, the electro-weak model boson component is inferred from the extra-dimensional degrees of freedom of an 8-dimensional space-time. Then, we fix how to reproduce geometrically the interaction between Standard Model fermions and gauge bosons, in the low energy limit.

 

 

On the geometrization of the electro-magnetic interaction for a spinning particle
Authors: Francesco Cianfrani, Irene Milillo, Giovanni Montani
Speaker: Francesco Cianfrani

We outline that, in a Kaluza-Klein framework, not only the electro-magnetic field can be geometrized, but also the dynamics of a charged spinning particle can be inferred from the motion in a 5-dimensional space-time. This result is achieved by the dimensional splitting of Papapetrou equations and by proper identifications of four-dimensional quantities. Then, since in such a context an electric dipole moment arises, we provide explanations for the induced parity and time-reversal violations consequently implied in a quantum framework.

 

 

Hamiltonian formulation of the 5-D Kaluza-Klein model and test-particle motion.
Authors: Valentino Lacquaniti, Giovanni Montani
Speaker: Valentino Lacquaniti

We examine the ADM reformulation of the 5-D KK model: the KK reduction is provided to commute with the ADM splitting. In details, we determine how the time component of the gauge vector is given by combination of the Lagrangian multipliers for the 5-D gravitational field. We work out the explicit Hamiltonian and give some simple solutions for the metric field in the ADM picture. Finally, we consider the motion of test-particles in the 5-D scenario: the definition of charge leads to the usual electro-dynamics coupling after dimensional reduction; a time-varying fine structure constant is recognized because an extra scalar field is present in the 4-D theory.

 

 

Covariant Description of the Inhomogeneous Mixmaster Chaos
Authors: Giovanni Montani, Riccardo Benini
Speaker: Riccardo Benini

We outline the covariant nature of the chaos characterizing the generic cosmological solution near the initial singularity, i.e. the so-called inhomogeneous Mixmaster model. Our analysis is based on a ”gauge” independent ADM-reduction of the dynamics to the physical degrees of freedom. The out-coming picture shows how the inhomogeneous Mixmaster model is isomorphic point by point in space to a billiard on a Lobachevsky plane. The existence of an asymptotic (energylike) constant of the motion allows us to construct the Jacobi metric associated to the geodesic flow and to calculate a non-zero Lyapunov exponent in each space point. The chaos covariance emerges from the independence of our scheme of the form of the lapse function and the shift vector; the origin of this result relies on the dynamical decoupling of space points, which takes place near the singularity, due to the asymptotic approach of the potential term to infinite walls.

 

 

Vector Field Induced Chaos in Multi-dimensional Homogeneous Cosmologies
Authors: Riccardo Benini, Alexander A. Kirillov, Giovanni Montani
Speaker: Riccardo Benini

We show that in multidimensional gravity, vector fields completely determine the structure and properties of singularity. It turns out that, in presence of a vector field, the oscillatory regime exists for all homogeneous models in any number of space-time dimensions. By analyzing the Hamiltonian equations, we derive the Poincar return map associated with the Kasner indices and fix the rules according to which the Kasner vectors rotate. In correspondence to a fourdimensional space-time, the oscillatory regime here constructed overlaps the usual Belinski-Khalatnikov-Liftshitz one.

 

 

Classical and Quantum Aspects of the Inhomogeneous Mixmaster Chaoticity
Authors: Riccardo Benini and Giovanni Montani
Speaker: Riccardo Benini

The dynamics of the generic inhomogeneous Mixmaster is analyzed via an ADM-reduction of the Hamiltonian constraints and adopting Misner-Chitre-like variables. We establish that, near the Big-Bang, the evolution of the system is isomorphic to a billiard on a Lobachevski plane and the corresponding microcanonical distribution is calculated. The comparison between the continuity equation on the ensemble and the WKB semi-classical limit of the Schrodinger equation fixes the normal ordering procedure. Finally, the features of the full quantum dynamics, with particular attention to the ground state level, are outlined.

 

 

Stability of an Isotropic Viscous Universe
Authors: Nakia Carlevaro, Giovanni Montani
Speaker: Nakia Carlevaro

We present a discussion of the effects induced by the bulk viscosity on the very early Universe stability. The matter filling the cosmological (isotropic and homogeneous) background is described by an ultra-relativistic viscous fluid whose viscosity coefficient is related to the energy density via a power-law of the form  = 0. The analytic expression of the density contrast (obtained for  = 1/2) shows that, for small values of the constant 0, its behavior is not significantly different from the non-viscous one derived by E.M. Lifshitz. But as soon as this constant overcomes a critical value, the growth of the density contrast is suppressed forward in time. On the other hand, in such a regime, the asymptotic approach to the initial singularity is deeply modified by the appearance of significant viscosity in the primordial thermal bath, i.e. the isotropic and homogeneous Universe admits an unstable collapsing picture. In our model this feature concernes also scalar perturbations while in the non-viscous case it appears only for tensor modes.

 

 

Viscous Features of a Gas Cloud Gravitational Collapse
Authors: Nakia Carlevaro, Giovanni Montani
Speaker: Nakia Carlevaro

We analyze the effects induced by the bulk viscosity on the dynamics associated to the extreme gravitational collapse. The work is aimed to investigate whether the presence of viscous corrections to the evolution of a collapsing gas cloud influences the top-down fragmentation process. For this purpose, we generalize the approach presented by C. Hunter to include in the dynamics of a uniform and spherically symmetric cloud; the negative pressure contribution associated to the bulk viscosity phenomenology is taken into account in the dynamics. Within the framework of a Newtonian approach (whose range of validity is outlined), we extend to the viscous case both the Lagrangian and the Eulerian motion of the system, and we treat the viscosity coefficient as related to the density via a power-law of the form  = 05/6. We remark how, in the adiabatic-like regime, density contrasts acquire asymptotically a vanishing behavior, which prevents the formation of sub-structures. Since in the non-dissipative case density contrasts diverge, we can conclude that the top-down mechanism of structure formation is suppressed as enough viscous effects are taken into account (such a feature is not present in the isothermal-like collapse).

 

 

Generic Evolutionary Quantum Cosmology
Authors: Valerio Battisti, Giovanni Montani
Speaker: Valerio Battisti

The implications of Evolutionary Quantum Gravity are addressed in view of the formulation of a new dark matter candidate. We consider a Schr¨odinger dynamics for the gravitational field associated to a generic cosmological model and then we solve the corresponding eigen-values problem. We emphasize that, when a Planckian cut-off is imposed in the theory and the classical limit of the ground state is taken, then a dark matter contribution cannot arise today. Summarizing, we fix that, from a phenomenological point of view, an Evolutionary Quantum Cosmology overlaps the Wheeler-DeWitt approach.

 

 

Is Torsion a Fundamental Physical Field?
Author: Simone Mercuri, Giovanni Montani
Speaker: Simone Mercuri

The introduction of Torsion in the framework of Einstein’s theories is in general motivated by no gauge principle. But the invariance of the gravitational interaction under the group of diffeomorphisms obliges to consider not only the usual ”pure” local Lorentz invariance but also the local rotations generated by the diff. group on the spinor bundle. This allows us to introduce two Lorentz valued connections: the spin connection and the contortion tensor. Our theory gives a gauge motivation to introduce Torsion and reduces the four-spinor interaction term of Einstein-Cartan theory to a usual vector gauge interaction.

 

 

Nieh-Yan invariant and Fermions in Ashtekar- Barbero-Immirzi formalism.
Author: Simone Mercuri
Speaker: Simone Mercuri

The Ashtekar-Barbero-Immirzi formulation of General Relativity is extended to include spinor matter fields. It is demonstrated that the consistency of the coupled system requires the introduction of a non-minimal coupling term in the action of the Dirac field. The non-minimal interaction and the Holst modification to the Hilbert-Palatini action reconstruct the Nieh-Yan invariant. Hence all the terms depending on the Immirzi parameter turn out to be encoded in the Nieh-Yan term, which reduces to a total divergence not affecting the classical dynamics. It is worth specifying that the structure of the total action allows us to split it in the self and the anti-self dual part, simplifying the calculation and the structure of the constraints.