Radiatively Induced Breaking of Conformal Symmetry in a Superpotential

Radiatively induced symmetry breaking is considered for a toy model with one scalar and one fermion field unified in a superfield. It is shown that the classical quartic self-interaction of the superfield possesses a quantum infrared singularity. Application of the Coleman-Weinberg mechanism for effective potential leads to the appearance of condensates and masses for both scalar and fermion components. That induces a spontaneous breaking of the initial classical symmetries: the supersymmetry and the conformal one. The energy scales for the scalar and fermion condensates appear to be of the same order, while the renormalization scale is many orders of magnitude higher. A possibility to relate the considered toy model to conformal symmetry breaking in the Standard Model is discussed.Comment: Improved final version with new references and misprints corrected, 9 pages , no figure

New spherically symmetric monopole and regular solutions in Einstein-Born-Infeld theories

In this work a new asymptotically flat solution of the coupled Einstein-Born-Infeld equations for a static spherically symmetric space-time is obtained. When the intrinsic mass is zero the resulting spacetime is regular everywhere, in the sense given by B. Hoffmann and L. Infeld in 1937, and the Einstein-Born-Infeld theory leads to the identification of the gravitational with the electromagnetic mass. This means that the metric, the electromagnetic field and their derivatives have not discontinuities in all the manifold. In particular, there are not conical singularities at the origin, in contrast to well known monopole solution studied by B. Hoffmann in 1935. The lack of uniqueness of the action function in Non-Linear-Electrodynamics is discussed.Comment: Final version in journal. Amplied version with new results that previous talk in Protvino worksho

The Newman-Janis Algorithm, Rotating Solutions and Einstein-Born-Infeld Black Holes

A new metric is obtained by applying a complex coordinate trans- formation to the static metric of the self-gravitating Born-Infeld monopole. The behaviour of the new metric is typical of a rotating charged source, but this source is not a spherically symmetric Born-Infeld monopole with rotation. We show that the structure of the energy-momentum tensor obtained with this new metric does not correspond to the typical structure of the energy momentum tensor of Einstein-Born-Infeld theory induced by a rotating spherically symmetric source. This also show, that the complex coordinate transformations have the interpretation given by Newman and Janis only in space-time solutions with linear sources

Von Neumann's Quantization of General Relativity

Von Neumann's procedure is applied for quantization of General Relativity. We quantize the initial data of dynamical variables at the Planck epoch, where the Hubble parameter coincides with the Planck mass. These initial data are defined via the Fock simplex in the tangent Minkowskian space-time and the Dirac conformal interval. The Einstein cosmological principle is applied for the average of the spatial metric determinant logarithm over the spatial volume of the visible Universe. We derive the splitting of the general coordinate transformations into the diffeomorphisms (as the object of the second N\"other theorem) and the initial data transformations (as objects of the first N\"other theorem). Following von Neumann, we suppose that the vacuum state is a quantum ensemble. The vacuum state is degenerated with respect to quantum numbers of non-vacuum states with the distribution function that yields the Casimir effect in gravidynamics in analogy to the one in electrodynamics. The generation functional of the perturbation theory in gravidynamics is given as a solution of the quantum energy constraint. We discuss the region of applicability of gravidynamics and its possible predictions for explanation of the modern observational and experimental data.Comment: 14 pages, updated version with extended discussio

Algebraic Bethe Ansatz for deformed Gaudin model

The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a recurrence relation. The commutation relations between the generating function t(\lambda) of the integrals of motion and the creation operators are calculated and therefore the algebraic Bethe Ansatz is fully implemented. The energy spectrum as well as the corresponding Bethe equations of the system coincide with the ones of the sl_2-invariant Gaudin model. As opposed to the sl_2-invariant case, the operator t(\lambda) and the Gaudin Hamiltonians are not hermitian. Finally, the inner products and norms of the Bethe states are studied.Comment: 23 pages; presentation improve

Rotation and twist regular modes for trapped ghosts

A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum $J\neq 0$ and twist modes. It is found that the rotation mode, which has no parity, causes excess in the angular velocity of dragged distant coordinate frames in one sheet of the wormhole while in the other sheet the angular velocity of the ghosts is that of rotating stars: $2J/r^3$. As to the twist modes, which all have parity, they cause excess in the angular velocity of one of the throat's poles with respect to the other.Comment: 11 pages, 3 figures; General Relativity and Gravitation - 201