Minisuperspace Model for Revised Canonical Quantum Gravity

We present a reformulation of the canonical quantization of gravity, as referred to the minisuperspace; the new approach is based on fixing a Gaussian (or synchronous) reference frame and then quantizing the system via the reconstruction of a suitable constraint; then the quantum dynamics is re-stated in a generic coordinates system and it becomes dependent on the lapse function. The analysis follows a parallelism with the case of the non-relativistic particle and leads to the minisuperspace implementation of the so-called {\em kinematical action} as proposed in \cite{M02} (here almost coinciding also with the approach presented in \cite{KT91}). The new constraint leads to a Schr\"odinger equation for the system. i.e. to non-vanishing eigenvalues for the super-Hamiltonian operator; the physical interpretation of this feature relies on the appearance of a ``dust fluid'' (non-positive definite) energy density, i.e. a kind of ``materialization'' of the reference frame. As an example of minisuperspace model, we consider a Bianchi type IX Universe, for which some dynamical implications of the revised canonical quantum gravity are discussed. We also show how, on the classical limit, the presence of the dust fluid can have relevant cosmological issues. Finally we upgrade our analysis by its extension to the generic cosmological solution, which is performed in the so-called long-wavelength approximation. In fact, near the Big-Bang, we can neglect the spatial gradients of the dynamical variables and arrive to implement, in each space point, the same minisuperspace paradigm valid for the Bianchi IX model.Comment: 16 pages, no figures, to appear on International Journal of Modern Physics

General Relativity as Classical Limit of Evolutionary Quantum Gravity

We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that a non-vanishing behavior of the Hamiltonian comes out. We then interpret such resulting non-zero ``energy'' of the gravitational field in terms of a dust fluid. This new matter contribution is co-moving to the slicing and it accounts for the ``materialization'' of a synchronous reference from the corresponding gauge condition. Further, we analyze the quantum dynamics of a generic inhomogeneous Universe as described by this evolutionary scheme, asymptotically to the singularity. We show how the phenomenology of such a model overlaps the corresponding Wheeler-DeWitt picture. Finally, we study the possibility of a Schr\"odinger dynamics of the gravitational field as a consequence of the correspondence inferred between the ensemble dynamics of stochastic systems and the WKB limit of their quantum evolution. We demonstrate that the time dependence of the ensemble distribution is associated with the first order correction in $\hbar$ to the WKB expansion of the energy spectrum.Comment: 23 pages, to appear on Class. Quant. Gra

Towards Loop Quantum Gravity without the time gauge

The Hamiltonian formulation of the Holst action is reviewed and it is provided a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the Loop Quantum Gravity quantization procedure can be applied when the time-gauge condition does not stand.Comment: 5 pages, accepted for publication in Phys. Rev. Let

Synchronous Quantum Gravity

The implications of restricting the covariance principle within a Gaussian gauge are developed both on a classical and a quantum level. Hence, we investigate the cosmological issues of the obtained Schr\"odinger Quantum Gravity with respect to the asymptotically early dynamics of a generic Universe. A dualism between time and the reference frame fixing is then inferred.Comment: 8 pages, Proceedings of the II Stueckelberg worksho

Fueled by a Fearful Leader: When, to What Extent and How Leader Fear of COVID-19 Promotes Employee Performance

The literature generally surmises that negative affective states of leaders are detrimental to leader effectiveness and work outcomes. Taking the opposite view, this study explores how the negative affective experiences of leaders related to COVID-19 may foster team commitment and employee performance. By integrating personality systems interaction theory, cognitive appraisal theory, and the literature on stress-based emotions, we develop a model that clarifies when, how, and to what extent leader fearful states related to COVID-19 drive employee performance. Using three-wave and multisource data from 579 employees and their leaders from 69 teams, we found that among leaders who exhibited higher levels of positive affectivity, leader fear of COVID-19 indirectly fostered employee performance via the mediating roles of leader promotion of team goals and team commitment. Moreover, these moderated indirect effects were strongest at moderate levels of leader fear of COVID-19. We discuss the theoretical and practical implications of these findings for research on leader affective states

Shortcomings of the Big Bounce derivation in Loop Quantum Cosmology

We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time. This procedure allows to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in Loop Quantum Cosmology. This feature makes the super-Hamiltonian regularization an open issue of the whole formulation.Comment: 4 pages, accepted for publication in Phys. Rev. D as a Rapid Communicatio

Quantum mechanics over a q-deformed (0+1)-dimensional superspace

We built up a explicit realization of (0+1)-dimensional q-deformed superspace coordinates as operators on standard superspace. A q-generalization of supersymmetric transformations is obtained, enabling us to introduce scalar superfields and a q-supersymmetric action. We consider a functional integral based on this action. Integration is implemented, at the level of the coordinates and at the level of the fields, as traces over the corresponding representation spaces. Evaluation of these traces lead us to standard functional integrals. The generation of a mass term for the fermion field leads, at this level, to an explicitely broken version of supersymmetric quantum mechanics.Comment: 11 pages, Late

Dark Matter Prediction from Canonical Quantum Gravity with Frame Fixing

We show how, in canonical quantum cosmology, the frame fixing induces a new energy density contribution having features compatible with the (actual) cold dark matter component of the Universe. First we quantize the closed Friedmann-Robertson-Walker (FRW) model in a sinchronous reference and determine the spectrum of the super-Hamiltonian in the presence of ultra-relativistic matter and a perfect gas contribution. Then we include in this model small inhomogeneous (spherical) perturbations in the spirit of the Lemaitre-Tolman cosmology. The main issue of our analysis consists in outlining that, in the classical limit, the non-zero eigenvalue of the super-Hamiltonian can make account for the present value of the dark matter critical parameter. Furthermore we obtain a direct correlation between the inhomogeneities in our dark matter candidate and those one appearing in the ultra-relativistic matter.Comment: 5 pages, to appear on Modern Physics Letters

Implications of the gauge-fixing in Loop Quantum Cosmology

The restriction to invariant connections in a Friedmann-Robertson-Walker space-time is discussed via the analysis of the Dirac brackets associated with the corresponding gauge fixing. This analysis allows us to establish the proper correspondence between reduced and un-reduced variables. In this respect, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if edges are parallel to simplicial vectors and the quantization of the model is performed via standard techniques by restricting admissible paths. Within this scheme, the discretization of the area spectrum is emphasized. Then, the role of the diffeomorphisms generator in reduced phase-space is investigated and it is clarified how it implements homogeneity on quantum states, which are defined over cubical knots. Finally, the perspectives for a consistent dynamical treatment are discussed.Comment: 7 pages, accepted for publication in Physical Review

Mean field and pairing properties in the crust of neutron stars

Properties of the matter in the inner crust of a neutron star are investigated in a Hartree-Fock plus BCS approximation employing schematic effective forces of the type of the Skyrme forces. Special attention is paid to differences between a homogenous and inhomogeneous description of the matter distribution. For that purpose self-consistent Hartree Fock calculations are performed in a spherical Wigner-Seitz cell. The results are compared to predictions of corresponding Thomas Fermi calculations. The influence of the shell structure on the formation of pairing correlations in inhomogeneous matter are discussed.Comment: 11 pages, 9 figure