Accelerated expansion from braneworld models with variable vacuum energy

We study the acceleration of the universe as a consequence of the time evolution of the vacuum energy in cosmological models based in braneworld theories in 5D. A variable vacuum energy may appear if the size of the extra dimension changes during the evolution of the universe. In this scenario the acceleration of the universe is related not only to the variation of the cosmological term, but also to the time evolution of G and, possibly, to the variation of other fundamental constants as well. This is because the expansion rate of the extra dimensionappears in different contexts, notably in expressions concerning the variation of rest mass and electric charge. We concentrate our attention on spatially-flat, homogeneous and isotropic, brane-universes where the matter density decreases as an inverse power of the scale factor, similar (but at different rate) to the power law in FRW-universes of general relativity. We show that these braneworld cosmologies are consistent with the observed accelerating universe and other observational requirements. In particular, G becomes constant and asymptotically in time. Another important feature is that the models contain no adjustable parameters. All the quantities, even the five-dimensional ones, can be evaluated by means of measurements in 4D. We provide precise constrains on the cosmological parameters and demonstrate that the effective equation of state of the universe can, in principle, be determined by measurements of the deceleration parameter alone. We give an explicit expression relating the density parameters , and the deceleration parameter q. These results constitute concrete predictions that may help in observations for an experimental/observational test of the model.     

Multipoint Series of Gromov–Witten Invariants of CP1

We derive explicit formulas for the multipoint series of in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of . We also obtain explicit formulas for the Hodge integrals , in the cases i=0 and 1.     

Some Remarks on the Smoluchowski–Kramers Approximation

According to the Smoluchowski–Kramers approximation, solution q _t of the equation , where is the White noise, converges to the solution of equation as µ 0. Many asymptotic problems for the last equation were studied in recent years. We consider relations between asymptotics for the first order equation and the original second order equation. Homogenization, large deviations and stochastic resonance, approximation of Brownian motion W _t by a smooth stochastic process, stationary distributions are considered.     

On the Modified Korteweg–De Vries Equation

We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg–de Vries equation , with initial data . We assume that the coefficient is real, bounded and slowly varying function, such that , where . We suppose that the initial data are real-valued and small enough, belonging to the weighted Sobolev space . In comparison with the previous paper (Internat. Res. Notices 8 (1999), 395–418), here we exclude the condition that the integral of the initial data u ₀ is zero. We prove the time decay estimates and for all , where . We also find the asymptotics for large time of the solution in the neighborhood of the self-similar solution.     

Born–Infeld Action in (n+2)-Dimension,the Field Equation and a Soliton Solution

In this Letter we introduce the (n+2)-dimensional Born–Infeld action with a dual field strength . We compute the field equation by using Schur polynomials and give a soliton solution.     

An electrical test particle in Einstein's unified field theory

Previous work on a class of exact solutions to the field equations of Einstein's unified field theory has shown that some of these solutions acquire an immediate physical meaning as soon as one allows for external sources, as it occurs in the general theory of relativity. It is evident that a four-current density j ⁱ , appended to the right-hand side of the field equation , has a fundamental role: in some solutions, a string built with this current density gives rise to partons, mutually interacting with forces that do not depend on distance, like the ones invoked to explain the confinement of quarks. In other solutions, for which obeys Maxwell's equations, jⁱ clearly displays electrical behavior. In the present paper it is shown under what conditions the electrical behavior of a charged test particle can be extracted from the field equations and from conservation identities related to the theory, when sources are appended in the way proposed by Borchsenius and Moffat.     

Classical Euclidean Wormhole Solution and Wave Function for a Nonlinear Scalar Field

In this paper we consider the classical Euclidean wormhole solution of the Born—Infeld scalar field. The corresponding classical Euclidean wormhole solution can be obtained analytically for both very small and large . At the extreme limit of small the wormhole solution has the same format as one obtained by Giddings and Strominger (Nuclear Physics B 306, 890, 1988). At the extreme limit of large the wormhole solution is a new one. The wormhole wave functions can also be obtained for both very small and large . These wormhole wave functions are regarded as solutions of quantum-mechanical Wheeler—Dewitt equation with certain boundary conditions.     

On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the configuration space of Yang-Mills theories is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that is contained in a zero measure subset of with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on . Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space .     

Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua

For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation ( NLSE), , with finite-density initial data

Dirac Equation in an Axial Coulomb Potential

We consider solutions to the Dirac equation in the presence of an external axial vector potential coupled to the spinor field psi through the interaction term . There turn out to be no bound-state energies in this system consistent with a normalizable wave function.     

Modified Weyl theory and extended elementary objects

To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R₀ appear as islands D_(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the domains D_(i), space-time is identified with the pseudo-Riemannian space of general relativity. Extension and symmetry breaking are described by a set of additional fields ( , given as a section on an associated bundle over space-time B with structural group = G D(1), where D(1) is the dilation group. Field equations for the quantities defining the underlying bundle geometry and for the fields are established involving matter source currents derived from a generalized spinor wave function. Einstein's equations for the metric are regarded as the part of the -gauge theory related to the Lorentz subgroup H of G exhibiting thereby the broken nature of the -symmetry for regions outside the domains D_(i).Talk presented at the International Conference on Field Theory and General Relativity held at Utah State University, Logan, Utah, June 26–July 2, 1988.     

Space-time symmetries of superstring and Jordan algebras

The sequence of Jordan algebras , whose elements are the 3×3 Hermitian matrices over the division algebras , , , and , is considered. These algebras are naturally related to supersymmetric structures in space-time dimensions of 3, 4, 6, and 10, as the Lorentz groups in these dimensions can be expressed in a unified way as a subgroup of the structure group of the Jordan algebras . The generators of the complete structure group and the automorphism group can be separated into bosonic and fermionic generators, depending on their transformation properties under the Lorentz subgroup. A peculiar connection between these fermionic generators and the supersymmetry generators of the superstring action is introduced and discussed.     

Separable coordinates for four-dimensional Riemannian spaces

We present a complete list of all separable coordinate systems for the equations and with special emphasis on nonorthogonal coordinates. Applications to general relativity theory are indicated.     

Finite Range of Large Perturbations in Hamiltonian Dynamics

The dynamics defined by the Hamiltonian , where the _m are fixed random phases, is investigated for large values of A, and for . For a given P ^* and for , this Hamiltonian is transformed through a rigorous perturbative treatment into a Hamiltonian where the sum of all the nonresonant terms, having a Q dependence of the kind cos(kQ – nt + _m) with \Delta \upsilon$$ " align="middle" border="0"> , is a random variable whose r.m.s. with respect to the _m is exponentially small in the parameter . Using this result, a rationale is provided showing that the statistical properties of the dynamics defined by H, and of the reduced dynamics including at each time t only the terms in H such that , can be made arbitrarily close by increasing . For practical purposes close to 5 is enough, as confirmed numerically. The reduced dynamics being nondeterministic, it is thus analytically shown, without using the random-phase approximation, that the statistical properties of a chaotic Hamiltonian dynamics can be made arbitrarily close to that of a stochastic dynamics. An appropriate rescaling of momentum and time shows that the statistical properties of the dynamics defined by H can be considered as independent of A, on a finite time interval, for A large. The way these results could generalize to a wider class of Hamiltonians is indicated.     

A New Approach to Spinors and Some Representations of the Lorentz Group on Them

We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the Lorentz group, which at the same time realize bosonic spin-1 and fermionic spin- wave equations of relativistic field theory, showing some unexpected relations between various low-dimensional Lorentz representations. We include a geometrically and physically motivated introduction to Jordan triples and spin factors.     

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy , we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) . We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in . We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's , which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.     

On General Plane Fronted Waves. Geodesics

A general class of Lorentzian metrics, , , with any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as , as in the classical model of exact gravitational waves.     

A Brief Guide to Variations in Teleparallel Gauge Theories of Gravity and the Kaniel-Itin Model

Recently Kaniel and Itin proposed a gravitational model with the wave type equation as vacuum field equation, where denotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corresponding mistakes in the literature. Then we turn to a detailed discussion of the Kaniel-Itin model.     

Energy Levels of Interacting Fields in a Box

We study the influence of boundary conditions on energy levels of interacting fields in a box and discuss some consequences when we hange the size of the box. In order to do this we calculate the energy levels of bound states of a scalar massive field nteracting with another scalar field through the Lagrangian = > in a one-dimensional box on which we impose Dirichlet boundary conditions. We find that the gap between the bound states changes with the size of the box in a nontrivial way. For the case where the masses of the two fields are equal and for large box the energy levels of Dashen-Hasslacher-Neveu (DHN model) are recovered and we have a kind of boson condensate for the ground state. Below a critical box size the ground-state level splits, which we interpret as particle-antiparticle production under small perturbations of box size. Below other critical sizes, and , of the box, the ground state and firstexcited state merge in the continuum part of the spectrum.