On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.     

Electrical studies of surface reconstruction resulting from chalcogen evaporation at the Ag2±δX/Vacuum interface (X=S, Se)X/Vacuum interface (X=S, Se)

We have investigated the dissociation rates of nonstoichiometric semiconductors Ag_2±δX (X=S, Se) to the vacuum by means of solid-state electrochemical technique. The values of chalcogen fluxes from the sample’s surface were measured versus compound’s composition and temperature. There has been obtained experimental evidence of the surface reconstruction of silver chalcogenides when the exact phase composition δ_cr.(T) is reached. This critical value δ_cr. correlates with the order-disorder transition in the silver sublattice for the Ag_2±δX/vacuum interface.     

Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.     

Dirac Quantization of t’Hooft-Polyakov Monopole Field: Axial Hamiltonization

In this article, we carry out the Hamiltonization in the axial gauge,of the t’Hooft-Polyakov monopole field outside the localized region, which represents the monopole’s core. One feature of the treatment here, is using the Higgs vacuum condition as both strong and weak equation instead of using it in the degree of freedom reduction.     

The Maxwell Electromagnetic Equations and the Lorentz Type Force Derivation—The Feynman Approach Legacy

R. Feynman’s “heretical” approach (Dyson in Am. J. Phys. 58:209–211, 1990; Dyson in Phys. Today 42(2):32–38, 1989) to deriving the Lorentz force based Maxwell electromagnetic equations is revisited, the its complete legacy is argued both by means of the geometric considerations and its deep relation with the vacuum field theory approach devised (Prykarpatsky et al. in Int. J. Theor. Phys. 49:798–820, 2010; Prykarpatsky et al. in Preprint ICTP, 2008, ). Being completely classical, we reanalyze the Feynman’s derivation from the classical Lagrangian and Hamiltonian points of view and construct its nontrivial relativistic generalization compatible with the vacuum field theory approach.     

A vacuum exterior to Maitra’s cylindrical dust solution

Maitra’s shearing, rotating cylindrical dust solution is fitted to a vacuum exterior. There are no closed timelike curves in the interior or exterior.     

On Verification of the Non-Generational Conjectural-Derivation of First Class Constraints: HP Monopole’s Field Case

In an earlier work we proposed a non-generational conjectural-derivation of all first class constraints (involving, only, variables compatible with canonical Poisson brackets) for “realistic” gauge (singular) field theories; and we verified the conjecture in cases of electromagnetic field, Yang-Mills fields interacting with scalar and spinor fields, and the gravitational field. Here, we will further verify our conjecture for the case of ’t Hooft-Polyakov (HP) monopole’s field (i.e. in the Higgs vacuum); and show that we will reproduce the results of Qandalji (Int. J. Theor. Phys. 45:1158, 2006), which were reached at using Dirac’s standard multi-generational algorithm.     

Standstill Electric Charge Generates Magnetostatic Field under Born-Infeld Electrodynamics

The Abelian Born-Infeld classical non-linear Electrodynamic has been used to investigate the electric and magnetostatic fields generated by a point-like electric charge at rest in an inertial frame. The results show a rich internal structure for the charge. Analytical solutions have also been found. Such fields configurations have been interpreted in terms of vacuum polarization and magnetic-like charges produced by the very high strengths of the electric field considered. Apparently non-linearity is responsible for the emergence of an anomalous magnetostatic field suggesting a possible connection to that created by a magnetic dipole composed of two magnetic charges with opposite signs. Consistently in situations where the Born-Infeld field strength parameter is free to become infinite, Maxwell’s regime takes over, the magnetic sector vanishes and the electric field assumes a Coulomb behavior with no trace of a magnetic component. The connection to other monopole solutions, like Dirac’s and ’tHooft’s Poliakov’s types are also discussed. Finally, some speculative remarks are presented in an attempt to explain such fields.     

Republication of: On the initial value problem of the equations of gravitation

This is an English translation of a paper by Karl Stellmacher, first published in German in 1938, in which he presented the first, correct and successful, formulation of the initial value problem for Einstein’s equations in vacuum and with a dust source. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Helmut Friedrich and Stellmacher’s brief biography written by Hubert Goenner.     

Birkhoff theorem and matter

Birkhoff’s theorem for spherically symmetric vacuum spacetimes is a key theorem in studying local systems in general relativity theory. However realistic local systems are only approximately spherically symmetric and only approximately vacuum. In a previous paper, we showed the theorem remains approximately true in an approximately spherically symmetric vacuum space time. In this paper we prove the other case: the theorem remains approximately true in a spherically symmetric, approximately vacuum space time.     

On Dark Energy,Weyl’s Geometry,Different Derivations of the Vacuum Energy Density and the Pioneer Anomaly

Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the (Anti) de Sitter solutions in terms of a family of radial functions R(r) that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared (UV/IR) entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of is derived in agreement with the experimental observations. A correct lower estimate of the mass of the observable universe related to the Dirac–Eddington–Weyl’s large number N = 10⁸⁰ is also obtained. The presence of the radial function R(r) is instrumental to understand why the cosmological constant is not zero and why it is so tiny. Finally, we rigorously prove why the proper use of Weyl’s Geometry within the context of Friedman–Lemaitre–Robertson–Walker cosmological models can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan–Brans–Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. The full theory involving the dynamics of Weyl’s gauge field A_μ is very rich and may explain also the anomalous Pioneer acceleration and the temporal variations (over cosmological scales) of the fundamental constants resulting from the expansion of the Universe. This is consistent with Dirac’s old idea of the plausible variation of the physical constants but with the advantage that it is not necessary to invoke extra dimensions. Dedicated to the loving memory of Rachael Bowers.     

Infraparticles with Superselected Direction of Motion in Two-Dimensional Conformal Field Theory

Particle aspects of two-dimensional conformal field theories are investigated, using methods from algebraic quantum field theory. The results include asymptotic completeness in terms of (counterparts of) Wigner particles in any vacuum representation and the existence of (counterparts of) infraparticles in any charged irreducible product representation of a given chiral conformal field theory. Moreover, an interesting interplay between the infraparticle’s direction of motion and the superselection structure is demonstrated in a large class of examples. This phenomenon resembles the electron’s momentum superselection expected in quantum electrodynamics.     

Homotopy Approach to Quantum Gravity

Gravity may be a quantum-space-time effect. General relativity is quantized by small generic changes in its commutation relations that make its Lie algebras simple on all levels, positing extra variables frozen by self-organization as needed. This quantizes space-time coordinates as well as fields and eliminates physical singularities. Fermi statistics and sl (nℝ) Lie algebras are assumed for all levels. Spin 1/2 is taken to be anomalous, arising from vacuum organization; the spin-statistics relation is incorporated. The gravitational field is quartic in Fermi variables. Einstein’s non-commutativity of parallel transport emerges as a vestige of Heisenberg’s quantum non-commutativity near the classical limit.     

On the Goldstonic gravitation theory

The physical specificity of gravity as a Goldstone-type field responsible for spontaneous breaking of space-time symmetries is investigated and extended up to supergravity. Problems of the Higgs gravitation vacuum and its matter sources are discussed. A particular “dislocation” structure of a space-time due to Poincaré translation gauge fields and the corresponding modification of Newton’s gravitational potential are predicted.     

Some Exact Bianchi Type-V Perfect Fluid Cosmological Models with Heat Flow and Decaying Vacuum Energy Density Λ: Expressions for Some Observable Quantities

In this paper we have obtained some new exact solutions of Einstein’s field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density Λ by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant Λ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for look-back time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Homotopic Classification of Yang–Mills Vacua Taking into Account Causality

Existence of θ-vacuum states in Yang–Mills theories defined over asymptotically flat space-times examined taking into account not only the topology but the complicated causal structure of these space-times, too. By a result of Galloway apparently causality makes all vacuum states, seen by a distant observer, homotopically equivalent making the introduction of θ-terms unnecessary. But a more careful analysis shows that certain twisted classical vacuum states survive even in this case eventually leading to the conclusion that the concept of “θ-vacua” is meaningful in the case of general Yang–Mills theories. We give a classification of these vacuum states based on Isham’s results showing that the Yang–Mills vacuum has the same complexity as in the flat Minkowskian case hence the general CP-problem is not more complicated than the well-known flat one. We also construct the θ vacua rigorously via geometric quantization. PACS numbers: 11.15, 11.30.E, 04.20.G, 04.70     

Non-static plane symmetric cosmological model in Wesson’s theory

The problem of non-static plane symmetric perfect fluid distribution in Wesson’s [1] scale invariant theory of gravitation with a time-dependent gauge function is investigated. The false vacuum model of the universe is constructed and some physical properties of the model are discussed.     

On stable variants of Einstein’s static universe

The investigation of the stability properties of certain variants of Einstein’s static universe performed by Carneiro and Tavakol (in Stability of the Einstein static universe in the presence of vacuum energy) is generalized. It is shown that all versions of Einstein’s static universe without interaction between the two fluids it contains are unstable. Interaction between the fluids may stabilize the universe. The condition for stability by perturbation of the scale factor from its static value is deduced for a class of universe models containing those investigated by Carneiro and Tavakol. Stability of the static state requires that energy is transformed to matter during such a perturbation.     

Vacuum fluctuations in charge–current uncertainty relations

We complete and justify the Bohr and Rosenfeld’s extension of their seminal work on the measurability of the free electromagnetic-field components to their pioneering paper on the measurement of charge–current uncertainty relations and the quantum control of vacuum fluctuations. We also show that it is possible to complete the aforementioned article with pseudo-realistic graphics of the thought experiments they designed.     

Effect of metallic surface microroughness on the probability and spectrum of plasmon excitation by a fast charged particle moving parallel to the surface

The Green’s function of the electric field of plasmons is determined in a semi-infinite medium with an abrupt plasma boundary where nonequilibrium conduction electrons either undergo elastic reflection from the boundary or “stick” to it and give rise to a stationary surface charge. The angular reflection of elastically scattered electrons can be either specular or diffuse. The Green’s function is used to find the singleevent spectrum of energy loss by a fast electron moving parallel to the boundary. The effect of electronboundary scattering parameters on the structure of bulk and surface plasmon resonances is analyzed. The probability of transition radiation of bulk plasmon by an electron moving in vacuum is examined. A new type of surface resonance is found under conditions of perfectly elastic scattering of conduction electrons from the plasma boundary, similar in structure to a tangential surface plasmon.