New Form of the T-Duality Due to the Stability of a Compact Dimension

We study behaviors of a compact dimension and the T-duality, in the presence of the wrapped closed bosonic strings. When the closed strings interact and form another system of strings, the radius of compactification increases. This modifies the T-duality, which we call it as T-duality-like. Some effects of the T-duality-like will be studied.     

A Comparison of the LVDP and ΛCDM Cosmological Models

We compare the cosmological kinematics obtained via our law of linearly varying deceleration parameter (LVDP) with the kinematics obtained in the ΛCDM model. We show that the LVDP model is almost indistinguishable from the ΛCDM model up to the near future of our universe as far as the current observations are concerned, though their predictions differ tremendously into the far future.     

Bulk Viscous Bianchi Type I Cosmological Models with Time-Dependent Cosmological Term Λ

Bianchi type I cosmological models with time-varying cosmological constant Λ and bulk viscous fluid are investigated. Cosmic matter is chosen to obey a barotropic equation of state. Exact solutions of Einstein’s field equations are obtained assuming the volume expansion θ proportional to the eigen values of shear tensor σ _ij . Physical and kinematical properties of the models are discussed considering bulk viscosity to be a power function of matter density.     

Bulk Viscous Bianchi Type V Cosmological Models with Decaying Cosmological Term Λ

We present bulk viscous Bianchi type V cosmological models with time-dependent cosmological term Λ. Exact solutions of Einstein field equations have been obtained by assuming shear scalar σ proportional to volume expansion θ. The coefficient of bulk viscosity is taken to be power function of energy density ρ or volume expansion θ. In these models cosmological term Λ come out to be negative. It is found that models obtained are expanding, shearing and non-rotating. They do not approach isotropy for large values of time t. Some observational parameters for the model have also been discussed.     

Effects Due to a Scalar Coupling on the Particle-Antiparticle Production in the Duffin-Kemmer-Petiau Theory

The Duffin-Kemmer-Petiau formalism with vector and scalar potentials is used to point out a few misconceptions diffused in the literature. It is explicitly shown that the scalar coupling makes the DKP formalism not equivalent to the Klein-Gordon formalism or to the Proca formalism, and that the spin-1 sector of the DKP theory looks formally like the spin-0 sector. With proper boundary conditions, scattering of massive bosons in an arbitrary mixed vector-scalar square step potential is explored in a simple way and effects due to the scalar coupling on the particle-antiparticle production and localization of bosons are analyzed in some detail.     

The Quantum Evolution of the Closed Friedman Universe with “Bouncing Off”

The homogeneous and isotropic closed Friedmanuniverse evolution in higher-order gravity theories isconsidered. The model takes into account vacuumpolarisation of conformal and nonconformal fields. That leads to the following addition in the Einsteinlagrangian: R² ln |R/R₀|. Near theregular minimum of the scale factor the model has ananalytical solution depending on an integration constantC. If |R/R₀| > 1, the solution passes through the regularminimum, experiences inflation with a decreasing valueof R and approaches to the critical value R =R₀. In the interval |R/R₀| < 1,the solutions have non-linear oscillations (i.e. the scalaronstage). On this stage of the evolution the universe isfilled with relativistic plasma. The continuoustransition through the critical point R = R₀is possible in only one type of solution, the separatrix.Though other solutions have no features in this point,they experience the discontinuity in derivatives of R.It is unsuitable since higher-order gravity theories are considered. Thus the measure of continuoussolutions giving a hot universe is negligible. Howeversolutions of the model can be continued in the imaginarytime. In such a case the Euclidean action will have a non-zero value because of the spaceclosed boundedness of the universe and the finiteness ofthe imaginary time interval (instanton). The last allowsus to calculate the probability of the quantum tunnelling of the Friedman universe from theinflation region into the scalaron region.     

Bianchi Type-III Cosmological Models with Gravitational Constant G and the Cosmological Constant ∧

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅲ universe by assuming conservation law for the energy-momentum tensor. Exact solutions of the field equations are obtained by using the scalar of expansion proportional to the shear scalar θ∝σ, which leads to a relation between metric potential B = Cn, where n is a constant. The corresponding physical interpretation of the cosmological solutions are also discussed.     

Scenario of Inflationary Cosmology from the Phenomenological Λ Models

Choosing the three phenomenological models of the dynamical cosmological term Λ, viz., , and Λ∼ρ where a is the cosmic scale factor, it has been shown by the method of numerical analysis for the considered non-linear differential equations that the three models are equivalent for the flat Universe k=0 and for arbitrary non-linear equation of state. The evolution plots for dynamical cosmological term Λ vs. time t and also the cosmic scale factor a vs. t are drawn here for k=0,+1. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.     

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.     

Quantization of Two Classical Models by Means of the BRST Quantization Method

An elementary gauge-non-invariant model and the bosonized form of the chiral Schwinger model are introduced as classical theories. The constraint structure is then investigated. It is shown that by introducing a new field, these models can be made gauge-invariant. The BRST form of quantization is reviewed and applied to each of these models in turn such that gauge-invariance is not broken. Some consequences of this form of quantization are discussed.     

The Foundations of Quantum Mechanics and the Evolution of the Cartan-Kähler Calculus

In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons. The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his calculus by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent. A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms.     

On the Stability of a Class of Modified Gravitational Models

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting is investigated. Specifically, after revisiting the f(R) case, R being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized type F(R,G,Q), G and Q being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is presented.     

Corrections to the Nonrelativistic Ground Energy of a Helium Atom

Considering the nuclear motion, we present the nonrelativistic ground energy of a helium atom by using a simple effective variational wavefunction with a flexible parameter k. Based on the result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be --2.90338 a.u. with the relative error 0.00034%.     

Cosmological evolution of interacting dark energy in Lorentz violation

The cosmological evolution of an interacting scalar-field model in which the scalar field interacts with dark matter, radiation, and baryons via Lorentz violation is investigated. We propose a model of interaction through the effective coupling, [`(b)]\bar{\beta} . Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar-field dark energy exist and baryons are subdominant. Secondly, the model also allows for the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through [`(b)]\bar{\beta} . In particular, we consider the simple case where [`(b)]\bar{\beta} has a quadratic form and has a good agreement with the modified ΛCDM and quintessence models. Finally, we also calculate the first post-Newtonian parameters for our model.     

Corrections to the effective orbital g-factor of diatomic 1Δ states

Anisotropies in the diamagnetic susceptibilities of coronene, anthracene and chrysene are reported. They have been determined from the quadrupolar magnetic field effect on the ²H N.M.R. spectra of the compounds. Results from this method are compared with those obtained from other techniques and the differences are discussed.     

Inducing the Cosmological Constant from Five-Dimensional Weyl Space

We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following the approach of the space-time-matter theory we show that when we go down from five to four dimensions, the Weyl field may contribute both to the induced energy-tensor as well as to the cosmological constant Λ, or more generally, it may generate a time-dependent cosmological parameter Λ(t). As an application, we construct a simple cosmological model in which Λ(t) has some interesting properties.     

A Plane-Symmetric Magnetized Inhomogeneous Cosmological Models of Perfect Fluid Distribution with Variable Magnetic Permeability in Lyra Geometry

A plane-symmetric magnetized inhomogeneous cosmological model of the universe with time dependent gauge function β for perfect fluid distribution with variable magnetic permeability within the framework of Lyra geometry is investigated. The source of the magnetic field is due to an electric current produced along the z-axis. Thus F ₁₂ is the only non-vanishing component of electromagnetic field tensor F _ij . To get a deterministic solution of Einstein’s modified field equations, the free gravitational field is assumed to be Petrov type-II non-degenerate. For our derived model we obtain the deceleration parameter q=−1 as in the case of de Sitter universe. It has been found that the displacement vector β(t) behaves like cosmological term Λ in the normal gauge treatment and the solution is consistent with the observations. The displacement vector β(t) affects entropy. Some physical and geometric properties of the model are also discussed.     

Some Ideas About Quantitative Convergence of Collision Models to Their Mean Field Limit

We consider a stochastic N-particle model for the spatially homogeneous Boltzmann evolution and prove its convergence to the associated Boltzmann equation when N⟶∞, with non-asymptotic estimates: for any time T>0, we bound the distance between the empirical measure of the particle system and the measure given by the Boltzmann evolution in a relevant Hilbert space. The control got is Gaussian, i.e. we prove that the distance is bigger than xN ^−1/2 with a probability of type O(e^-x2)O(e^{-x^{2}}). The two main ingredients are a control of fluctuations due to the discrete nature of collisions and a kind of Lipschitz continuity for the Boltzmann collision kernel. We study more extensively the case where our Hilbert space is the homogeneous negative Sobolev space [(H)\dot]^-s\smash {\dot {H}}^{-s}. Then we are only able to give bounds for Maxwellian models; however, numerical computations tend to show that our results are useful in practice.     

Coexistence of Ordered and Disordered Phases in Potts Models in the Continuum

This is the second of two papers on a continuum version of the Potts model, where particles are points in ℝ ^d , d≥2, with a spin which may take S≥3 possible values. Particles with different spins repel each other via a Kac pair potential of range γ ⁻¹, γ>0. In this paper we prove phase transition, namely we prove that if the scaling parameter of the Kac potential is suitably small, given any temperature there is a value of the chemical potential such that at the given temperature and chemical potential there exist S+1 mutually distinct DLR measures.