Some structurological remarks on a nonlocal field

In this paper, continued from the last paper (Ikeda, 1974), two kinds of structurological generalizations of our nonlocal field (i.e., the (x, ψ) field) are considered physicogeometrically. One is a Finslerian generalization, where the base field [i.e., the (x) field] is extended to a Finslerian field and Weyl's gauge field (i.e., the electromagnetic potential) is physically identified with the directional vector adopted as the internal variable in the ordinary nonlocal field theory. Another is a generalization by which the spinor (ψ) itself is taken as an independent variable, where some inherent characteristics ofψ are fused into the spatial structure. The latter is regarded as a “nonlocalization” of the (x) field accomplished by attachingψ to each point, in the true sense of the word. Particularly, the spatial structures of these generalized nonlocal fields are described in detail.     

Finslerian generalization of the hypothesis of Riemannian geodesics for motion of test bodies. I

It is shown, under the most general conditions imposed on the Finslerian metric and on the Lagrangian density of the gravitational field, that the streamlines of a Finslerian perfect fluid are Finslerian geodesics and that the equation of continuity is satisfied. This result is interesting for analyzing the motion of test bodies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 87–91, September, 1981.     

Non-uniqueness Results for Critical Metrics of Regularized Determinants in Four Dimensions

The regularized determinant of the Paneitz operator arises in quantum gravity [see Connes in (Noncommutative geometry, 1994), IV.4.γ]. An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in (Commun Math Phys 178:301–309, 1996). A similar formula holds for Cheeger’s half-torsion, which plays a role in self-dual field theory [see Juhl in (Families of conformally covariant differential operators, q-curvature and holography. Progress in Mathematics, vol 275, 2009)], and is defined in terms of regularized determinants of the Hodge laplacian on p-forms (p < n/2). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in (Commun Math Phys 149:241–262, 1992), (Ann Math 142:171–212, 1995), (Commun Math Phys 189:655–665, 1997).     

A response to Murshed et al., J Nanopart Res (2010) 12:2007–2010

This brief communication provides a response to Murshed et al. (J Nanopart Res 12:2007–2010, 2010). We acknowledge that three of the equations in our original article (Doroodchi et al. J Nanopart Res 11:1501–1507, 2009) contained minor typographical errors. However, we confirm that these misprinted equations have no bearing on the results presented within that article. In addition, we would like to clarify that we do not challenge the methodology of Leong et al. (J Nanopart Res 8:245–254, 2006). Instead, we repeated their analysis using a more general form for the temperature field with continuity imposed across the particle–nanolayer–liquid interfaces and found that the solution reduces to the Renovated-Maxwell model.     

A Matter Dominated Navigation Universe in Accordance with the Type Ia Supernova Data

We investigate a matter dominated navigation cosmological model. The influence of a possible drift (wind) in the navigation cosmological model makes the spacetime geometry change from Riemannian to Finslerian. The evolution of the Finslerian Universe is governed by the same gravitational field equation with the familiar Friedmann-Robertson-Walker one. However, the change of space geometry from Riemannian to Finslerian supplies us a new relation between the luminosity distant and redshift. It is shown that the Hubble diagram based on this new relation could account for the observations on distant Type Ia supernovae.     

On the Theory of Gravitational Field in Finsler Spaces - II

Continuing the last paper [1], more detailed considerations are made on the spatial structure of the Finslerian gravitational field: firstly, a unified field between the external (x)-field and the internal (y)-field is constructed from a vector bundle-like standpoint, where the intrinsic behavior (i.e., δy) of the internal vector variable y is taken into account; secondly, the connection structure and the metrical structure are determined by setting the base and dual base properly in the unified field; thirdly, a compactification process of the internal field (i.e., a mapping process of the (y)-field on the (x)-field) is considered in order to realize a four-dimensional Finslerian structure.     

Holographic Dark Energy in Brans-Dicke Cosmology with Granda-Oliveros Cut-off

Motivated by the recent works of one of us (Karami and Fehri, Int. J. Theor. Phys. 49:1118, 2010; Phys. Lett. B 684:61, 2010), we study the holographic dark energy in Brans-Dicke gravity with the Granda-Oliveros cut-off proposed recently in literature. We find out that when the present model is combined with Brans-Dicke field the transition from normal state where w _D >−1 to the phantom regime where w _D <−1 for the equation of state of dark energy can be more easily achieved for than when resort to the Einstein field equations is made. Furthermore, the phantom crossing is more easily achieved when the matter and the holographic dark energy undergo an exotic interaction. We also calculate some relevant cosmological parameters and their evolution.     

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 Matter Dominated Navigation Universe in Accordance with the Type Ia Supernova Data

We investigate a matter dominated navigation cosmological model.The influence of a possible drift(wind) in the navigation cosmological model makes the spacetime geometry change from Riemannian to Finslerian.The evolution of the Finslerian Universe is governed by the same gravitational field equation with the familiar Friedmann-Robertson-Walker one.However,the change of space geometry from Riemannian to Finslerian supplies us a new relation between the luminosity distant and redshift.It is shown that the Hubble diagram based on this new relation could account for the observations on distant Type Ia supernovae.     

On the Theory of Gravitational Field in Finsler Spaces - III

From the vector bundle-like standpoint, the Finslerian gravitational field is regarded as the total space of the vector bundle whose fibre is the internal (y)-field spanned by vectors {y} (i.e., the so-called internal space spanned by {y}) and whose base is the external (x)-field spanned by points {x} (i.e., the Einstein's gravitational field). Along this line, in this paper, different from a previous paper [1], the so-called mapping process of the (y)-field on the (x)-field is not taken into account and following Miron's method [2, 3], the Finslerian field equations will be derived from the Einstein's field equation for the total space. Some physical considerations will be made on those field equations.     

Connection between Finslerian geodesics and the field equations

It is shown that the equations of the gravitational field in 1-form Finslerian space-time imply that the streamlines of an incoherent fluid are Finslerian geodesics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 70–74, February, 1981.     

Gravitational field equations based on Finsler geometry

The analysis of a previous paper (see Ref. 1), in which the possibility of a Finslerian generalization of the equations of motion of gravitational field sources was demonstrated, is extended by developing the Finslerian generalization of the gravitational field equations on the basis of the complete contractionK = K _lj ^lj of the Finslerian curvature tensorK _l ^j _hk (x, y). The relevant Lagrangian is constructed by the replacement of the directional variabley ⁱ inK by a vector fieldy ⁱ (x), so that the notion of osculation may be regarded as the key concept on which the approach is based. The introduction of the auxiliary vector fieldy ⁱ (x) is shown to be of physical significance, for the field equations refer not only to the proper field variables but also to a special coordinate system associated withy ⁱ (x) through the Clebsch representation of the latter. The status of the conservation laws proves to be similar to that in the theory of the Yang-Mills field. By choosing a special Finslerian metric function we elucidate in detail the structure of the field equations in the static case.     

String Cosmological Solutions in Self-Creation Theory of Gravitation

We have studied the problem of cosmic strings for Bianchi-I, II, VIII and IX string cosmological models in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self—creation theory of gravitation. We have obtained some classes of solutions by considering different functional form for metric potentials. It is also observed that due to the presence of scalar field, the power index ‘m’ of the metric coefficients has a range of values.     

Finslerian Solution for Static Spherically Symmetric Gravitational Field

The previous work [1–3] was aimed at demonstrating the natural and intrinsic relationship between the fibered Finslerian framework and the Yang-Mills gauge field theroy based on the SU(2)-group of internal symmetries. In the present paper we continue the approach and find a particular solution for the Finslerian-extended Einstein equations that relates to static and spherically symmetric gravitational field. Our treatment has been stimulated by the following question: does the Finslerian approach predict the effect of speed-of-light change under transition from one inertially moving laboratory to another? The accurate solution which answers this question in positive has been found.     

Quantum-Gravity Thermodynamics, Incorporating the?Theory of Exactly Soluble Active Stochastic Processes, with Applications

A re-visitation of QFT is first cited, deriving the Feynman integral from the theory of active stochastic processes (Glueck and Hueffler, Phys. Lett. B. 659(1–2):447–451, 2008; Hueffel and Kelnhofer, Phys. Lett. B 588(1–2):145–150, 2004). We factor the lie group “generator” of the inverse wavefunction over an entropy-maximizing basis. Performing term-by-term Ito-integration leads us to an analytical, evaluable trajectory for a charged particle in an arbitrary field given a Maximum-Entropy distribution. We generalize this formula to many-body electrodynamics. In theory, it is capable of predicting plasma’s thermodynamic properties from ionic spectral data and thermodynamic and optical distributions. Blessed with the absence of certain limitations (e.g., renormalization) strongly present in competing formalisms and the incorporation of research related to many different phenomena, we outline a candidate quantum gravity theory based on these developments.     

On Steady Distributions of Kinetic Models of Conservative Economies

We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat. Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state.     

Charged perfect fluids in the presence of a cosmological constant

We consider the static and spherically symmetric field equations of general relativity for charged perfect fluid spheres in the presence of a cosmological constant. Following work by Florides (J Phys A Math Gen 16:1419–1433, 1983) we find new exact solutions of the field equations, and discuss their mass radius ratios. These solutions, for instance, require the charged Nariai metric to be the vacuum part of the spacetime. We also find charged generalizations of the Einstein static universe and speculate that the smallness problem of the cosmological constant might become less problematic if charge is taken into account.     

Singular Harmonic Maps and Applications to General Relativity

The study of axially symmetric stationary multi-black-hole configurations and the force between co-axially rotating black holes involves, as a first step, an analysis on the “boundary regularity” of the so-called reduced singular harmonic maps. We carry out this analysis by considering those harmonic maps as solutions to some homogeneous divergence systems of partial differential equations with singular coefficients. Our results extend previous works by Weinstein (Comm Pure Appl Math 43:903–948, 1990; Comm Pure Appl Math 45:1183–1203, 1992) and by Li and Tian (Manu Math 73(1):83–89, 1991; Commun Math Phys 149:1–30, 1992; Differential geometry: PDE on manifolds, vol 54, pp. 317–326, 1993). This paper is based on the Ph.D. thesis of the author (Singular harmonic maps into hyperbolic spaces and applications to general relativity, PhD thesis, The State University of New Jersey, Rutgers, 2009).     

Bianchi Type-III Dark Energy Model in a Saez-Ballester Scalar-Tensor Theory

In this paper, we investigate Bianchi type-III universe which has dynamical energy density. We introduce three different skewness parameters along spatial directions to quantify the deviation of pressure from isotropy. We also assume that the skewness parameters are time dependent. The Saez-Ballester (J. Phys. Lett. A 113:467, 1986) field equations have been solved by applying a variation law for generalized Hubble’s parameter given by Bermann (Nuovo Cimento B 74:182, 1983). Some physical and kinematical properties of dark energy model are discussed.