Organizacja pracy poczty. Przegląd Zagadnień Łączności, 1963, nr 9 (24)

Opracowania na podstawie artykułó

Hamiltonian Analysis of Poincar\'e Gauge Theory: Higher Spin Modes

We examine several higher spin modes of the Poincar\'e gauge theory (PGT) of gravity using the Hamiltonian analysis. The appearance of certain undesirable effects due to non-linear constraints in the Hamiltonian analysis are used as a test. We find that the phenomena of field activation and constraint bifurcation both exist in the pure spin 1 and the pure spin 2 modes. The coupled spin-$0^-$ and spin-$2^-$ modes also fail our test due to the appearance of constraint bifurcation. The ``promising'' case in the linearized theory of PGT given by Kuhfuss and Nitsch (KRNJ86) likewise does not pass. From this analysis of these specific PGT modes we conclude that an examination of such nonlinear constraint effects shows great promise as a strong test for this and other alternate theories of gravity.Comment: 30 pages, submitted to Int. J. Mod. Phys.

Gravitational Lorentz Force and the Description of the Gravitational Interaction

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analog of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of General Relativity. The main conclusion is that scalar matter is able to feel anyone of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.Comment: Equations (44)-(47) correcte

On certain relationships between cosmological observables in the Einstein-Cartan gravity

We show that in the Einstein-Cartan gravity it is possible to obtain a relation between Hubble's expansion and the global rotation (vorticity) of the Universe. Gravitational coupling can be reduced to dimensionless quantity of order unity, fixing the scalar mass density and the resulting negative cosmological constant at spacelike infinity. Current estimates of the expansion and rotation (see also astro-ph/9703082) of the Universe favour the massive spinning particles as candidate particles for cold and hot dark matter. Nodland and Ralston vorticity (Phys. Rev. Lett. 78 (1997) 3043) overestimates the value favoured by the Einstein-Cartan gravity for three orders of magnitude.Comment: 7 pages, LaTeX styl

Semi-Teleparallel Theories of Gravitation

A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well as teleparallel geometry. Within this geometry, the kinematic quantities of preferred frames are associated with torsion fields. Using a variational method, it is shown in which way action functionals for this geometry can be constructed. For a special action the field equations are derived and the coupling to spinor fields is discussed.Comment: 14 pages, LaTe

Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited

We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the strategy. Using a translation into mean-payoff parity games, we prove that the problem of computing (the permissiveness of) a most permissive winning strategy is in NP intersected coNP. Along the way, we provide a new study of mean-payoff parity games. In particular, we prove that the opponent player has a memoryless optimal strategy and give a new algorithm for solving these games.Comment: 30 pages, revised versio

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Four-fermion interaction from torsion as dark energy

The observed small, positive cosmological constant may originate from a four-fermion interaction generated by the spin-torsion coupling in the Einstein-Cartan-Sciama-Kibble gravity if the fermions are condensing. In particular, such a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early Universe. We study how the torsion-induced four-fermion interaction is affected by adding two terms to the Dirac Lagrangian density: the parity-violating pseudoscalar density dual to the curvature tensor and a spinor-bilinear scalar density which measures the nonminimal coupling of fermions to torsion.Comment: 6 pages; published versio

Big bounce from spin and torsion

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density $\epsilon\propto gT^4$ was on the order of $n^2/m_\textrm{Pl}^2$ (in natural units), where $n\propto gT^3$ is the fermion number density and $g$ is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles ($g\approx 100$), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about $10^{32}$ times smaller than its present value, giving \approx 50 \mum. If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.Comment: 6 pages; published versio

Torsion Gravity: a Reappraisal

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing independent degrees of freedom. By using an active version of the strong equivalence principle, a possible solution to this conceptual question is reviewed. This solution favors ultimately the teleparallel point of view, and consequently the completeness of general relativity. A discussion of the consequences for gravitation is presented.Comment: RevTeX, 34 pages. Review article to be published by Int. J. Mod. Phys.