Reparametrization-Invariant Path Integral in GR and "Big Bang" of Quantum Universe

The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space-time is obtained. The region of validity of the Faddeev-Popov-DeWitt functional is studied. It is shown that the invariant content of general relativity as a constrained system can be covered by two "equivalent" unconstrained systems: the "dynamic" (with "dynamic" evolution parameter as the metric scale factor) and "geometric" (given by the Levi-Civita type canonical transformation to the action-angle variables where the energy constraint converts into a new momentum). "Big Bang", the Hubble evolution, and creation of matter fields by the "geometric" vacuum are described by the inverted Levi-Civita (LC) transformation of the geomeric system into the dynamic one. The particular case of the LC transformations are the Bogoliubov ones of the particle variables (diagonalizing the dynamic Hamiltonian) to the quasiparticles (diagonalizing the equations of motion). The choice of initial conditions for the "Big Bang" in the form of the Bogoliubov (squeezed) vacuum reproduces all stages of the evolution of the Friedmann-Robertson-Walker Universe in their conformal (Hoyle-Narlikar) versions.Comment: 21 pages, latex, 4 figures in postscrip

Magnetic Strings in Dilaton Gravity

First, I present two new classes of magnetic rotating solutions in four-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potential. The first class of solutions yields a 4-dimensional spacetime with a longitudinal magnetic field generated by a static or spinning magnetic string. I find that these solutions have no curvature singularity and no horizons, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. The net electric charge of the strings in these spacetimes is proportional to their velocities. Second, I obtain the ($n+1$)-dimensional rotating solutions in Einstein-dilaton gravity with Liouville-type potential. I argue that these solutions can present horizonless spacetimes with conic singularity, if one chooses the parameters of the solutions suitable. I also use the counterterm method and compute the conserved quantities of these spacetimes.Comment: 16 pages, no figure, references added, some minor correction

Experimental test for extra dimensions in Kaluza-Klein gravity

5D Kaluza-Klein gravity has several nonasymptotically flat solutions which generally, possessed both electric and magnetic charges. In this paper we suggest that these solutions can act as quantum virtual handles (wormholes) in spacetime foam models. By applying a sufficently large, external electric and/or magnetic field it may be possible to ``inflate'' these solutions from a quantum to a classical state. This effect would lead to a possible experimental signal for higher dimensions in multidimensional gravity.Comment: 11 pages, 3 PS.figures, REVTEX, the quality of the figures are improve

Topological classification of black Hole: Generic Maxwell set and crease set of horizon

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.Comment: 22 pages, 6 figure

Accelerated Levi-Civita-Bertotti-Robinson Metric in D-Dimensions

A conformally flat accelerated charge metric is found in an arbitrary dimension $D$. It is a solution of the Einstein-Maxwell-null fluid with a cosmological constant in $D \ge 4$ dimensions. When the acceleration is zero our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that the charge loses its energy, for all dimensions, due to the acceleration.Comment: Latex File, 12 page

On the electrodynamics of moving bodies at low velocities

We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean electromagnetism

Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical generalization of the MICZ-Kepler system with linear and $\cos\theta$ potential terms. We also present the generalization of the parabolic coordinates, in which this system admits the separation of variables. Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page

COVID-19 vaccine mRNABNT162b2 elicits human antibody response in milk of breastfeeding women

Objective: The objective of this research is to demonstrate the release of SARS-CoV-2 Spike (S) antibodies in human milk samples obtained by patients who have been vaccinated with mRNABNT162b2 vaccine. Methods: Milk and serum samples were collected in 10 volunteers 20 days after the first dose and 7 seven days after the second dose of the mRNABNT162b2 vaccine. Anti-SARS-CoV-2 S antibodies were measured by the Elecsys® Anti-SARS-CoV-2 S ECLIA assay (Roche Diagnostics AG, Rotkreuz, Switzerland), a quantitative electrochemiluminescence immunometric method. Results: At first sample, anti-SARS-CoV-2 S antibodies were detected in all serum samples (103.9 ± 54.9 U/mL) and only in two (40%) milk samples with a low concentration (1.2 ± 0.3 U/mL). At the second sample, collected 7 days after the second dose, anti-SARS-CoV-2 S antibodies were detected in all serum samples (3875.7 ± 3504.6 UI/mL) and in all milk samples (41.5 ± 47.5 UI/mL). No correlation was found between the level of serum and milk antibodies; the milk antibodies/serum antibodies ratio was on average 2% (range: 0.2–8.4%). Conclusion: We demonstrated a release of anti-SARS-CoV-2 S antibodies in the breast milk of women vaccinated with mRNABNT162b2. Vaccinating breastfeeding women could be a strategy to protect their infants from COVID-19 infection

Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

The Maupertuis principle and canonical transformations of the extended phase space

We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals of motion, Lax equations, separated variables and action-angles variables. In this review we will discuss namely these induced transformations instead of the various parametric form of the geometric objects