International Journal of Modern Physics D

The Palatini variational method breaks down in 2D: First order forms of the Einstein action do not fix the affinity completely, as they possess an additional, Weyl, invariance absent in the second order versions.

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets. These probabilities generally cannot be given by the ordinary quantum “probabilities” for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth.

The quantization of supergravity is discussed using a canonical approach, in which one solves the supersymmetry constraints S_AΨ=0, where Ψ is a physical state. It appears, using an approach which involves auxiliary fields, that the amplitude to go from initial to final gravitational data (with zero gravitino data) is Ψ=exp(−I_B/ħ), where I_B is the classical Einstein-Hilbert action. This then suggests that fermionic amplitudes (including gravitino boundary data) may also be finite.

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge equivalent connections. This calculus does not use any background fields (such as a metric) and thus well-suited to a fully non-perturbative treatment of quantum gravity. Using this framework, quantum geometry is examined. Fundamental excitations turn out to be one-dimensional, rather like polymers. Geometrical observables such as areas of surfaces and volumes of regions are purely discrete spectra. Continuum picture arises only upon coarse graining of suitable semi-classical states. Next, regulated quantum diffeomorphism constraints can be imposed in an anomaly-free fashion and the space of solutions can be given a natural Hilbert space structure. Progress has also been made on the quantum Hamiltonian constraint in a number of directions. In particular, there is a recent approach based on a generalized .Wick transformation which maps solutions to the Euclidean quantum constraints to those of the Lorentzian theory. These developments are summarized. Emphasis is on conveying the underlying ideas and overall pictures rather than technical details.

We review some recent work concerning the classical thermodynamics and quantum mechanics of charged black holes in generic 2-D dilaton gravity. The main result that has emerged from this work is an intriguing connection between the classical black hole entropy and the imaginary part of the WKB phase of energy and charge eigenstates in the corresponding quantum theory.

The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appeared to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking’s radiation in the limit of low temperatures both for large and nearly extreme Reissner-Nordstrom black holes. The above mentioned infinite degeneracy of the mass (energy) eigenvalues may appeared helpful in resolving the well known information paradox in the black hole physics.

In a series of papers Amati, Ciafaloni and Veneziano and ’t Hooft conjectured that black holes occur in the collision of two light particles at planckian energies. In this talk based on [10] we discuss a possible scenario for such a process by using the Chandrasekhar-Ferrari-Xanthopoulos duality between the Kerr black hole solution and colliding plane gravitational waves.

We review electric/magnetic duality in N=4 (and certain N=2) globally supersymmetric gauge theories and show how this duality, which relates strong to weak coupling, follows as a consequence of a string/string duality. Black holes, eleven dimensions and supermembranes also have a part to play in the big picture.

A review is given of BRST mechanisms through which theories carrying realisations of nonlinear gauge-algebra representations may also be viewed as realizing embeddings into larger gauge algebras. This process generalizes the familiar non-linear realisations of spontaneously-broken Lie-algebra gauge symmetries to ssupersymmetric and higher-spin chiral quantum gravity models.

We review the theory of higher-spin gauge fields in four and three space-time dimensions and present some new results on higher-spin gauge interactions of matter fields in two dimensions.

We review here some recent results that show that inflationary cosmological models must contain initial singularities. We also present a new singularity theorem. The question of the initial singularity re-emerges in inflationary cosmology because inflation is known to be generically futureeternal, It is natural to ask, therefore, if inflationary models can be continued into the infinite past in a non-singular way. The results that we discuss show that the answer to the question is “no.” This means that we cannot use inflation as a way of avoiding the question of the birth of the Universe. We also argue that our new theorem suggests — in a sense that we explain in the paper — that the Universe cannot be infinitely old.

Quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states is considered in the one-loop approximation of quantum cosmology. A universal effective action algorithm for the distribution function of chaotic inflationary cosmologies is derived for both of these states. The energy scale of inflation is calculated by finding a sharp probability peak in this distribution function for a tunnelling model driven by the inflaton field with large negative constant ξ of nonminimal interaction. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant H≃10⁻⁵mp, its quantum width ΔH/H≃10⁻⁵ and the number of inflationary e-foldings N≃60) are found to be in good correspondence with the observational status of inflation theory, provided the coupling constants of the theory are constrained by a condition which is likely to be enforced by the (quasi) supersymmetric nature of the sub-Planckian particle physics model.

One of the most beautiful concepts in theoretical physics was the idea of fridmons, the semi-closed worlds which from the outside look like an elementary particle, but which may contain the whole universe in their heart. This idea was developed 25 years ago by Markov and his collaborators [1]. In this paper I will discuss some related ideas which have been developed very recently in the context of inflationary cosmology. The first one is the possibility that magnetic monopoles and other topological defects in a certain class of theories inflate, become exponentially large, and unceasingly produce other inflationary monopoles. The second idea is the possibility that an infinitely large open inflationary universe may fit into an interior of a single bubble of a finite size produced during the false vacuum decay.

The tool of functional averaging over some “large” diffeomorphisms is used to describe quantum systems with constraints, in particular quantum cosmology, in the language of quantum Effective. Action. Simple toy models demonstrate a supposedly general phenomenon: the presence of a constraint results in “quantum repel” from the classical mass shell.

Two major apparently unrelated problems, that of the origin of time in the universe associated with quantum gravity and of the entropy in de Sitter cosmological models, are found to have their origin in a single physical phenomenon: the semi-classical tunneling through a classically forbidden region of the cosmological scale factor. In this region there is a mixing of the states of quantum matter and those of the semi-classical gravity which produces a thermal mixture of the matter states and hence an “entropy;” this same mixing effect brings about the conversion of a parametric time variable into a physical intrinsic time.