Renormalizable models with simple symmetry breaking

If to a Lagrangian density with invariance under a continuous group of linear transformations of the fields a term linear or bilinear in the fields is added, the symmetry is in general reduced and the currents associated with the original symmetry are only partially conserved. If the theory without the added term is renormalizable, the theory with that term also is, and the needed renormalization conditions are the essential content of the appropriate Ward-Takahashi-Kazes-Rivers identities. The case of symmetry breaking by a term linear in Bose fields (source term) is here analysed completely, in particular with respect to the nonsymmetric limit of vanishing source term, a particular Goldstone mode, and with respect to properties of the ground state energy density as a function of the strength of the source term. Induced and spontaneous breaking of a discrete symmetry are also treated.     

On the vierbein formalism of general relativity

Both the Einstein–Hilbert action and the Einstein equations are discussed under the absolute vierbein formalism. Taking advantage of this form, we prove that the “kinetic energy” term, i.e., the quadratic term of time derivative term, in the Lagrangian of the Einstein–Hilbert action is non-positive definitive. And then, we present two groups of coordinate conditions that lead to positive definitive kinetic energy term in the Lagrangian, as well as the corresponding actions with positive definitive kinetic energy term, respectively. Based on the ADM decomposition, the Hamiltonian representation and canonical quantization of general relativity taking advantage of the actions with positive definitive kinetic energy term are discussed; especially, the Hamiltonian constraints with positive definitive kinetic energy term are given, respectively. Finally, we present a group of gauge conditions such that there is not any second time derivative term in the ten Einstein equations.     

Effect of the third-order filter term on soliton interactions in soliton transmission systems with filters

The effect of the third-order filter term on soliton interactions in optical fibers with guiding filters is theoretically analyzed. We find that this term causes a significant difference to the interaction of solitons through filters among the regimes of without sliding, with up- and down-sliding frequencies of filters. It is shown that the interaction between solitons can be more effectively suppressed by up-sliding filters than that by down-sliding filters in the presence of the third-order filter term. Moreover, the third-order filter term is found to play a positive role in suppressing soliton interactions in the case of non-sliding.     

Cosmological models with Yang-Mills fields

Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solution, even in absence of the cosmological constant term.     

Divergence formulation of source term

In this paper, we propose to write a source term in the divergence form. A conservation law with a source term can then be written as a single divergence form. We demonstrate that it enables to discretize both the conservation law and the source term in the same framework, and thus greatly simplifies the construction of numerical schemes. To illustrate the advantage of the divergence formulation, we apply the new formulation to construct a uniformly third-order accurate edge-based finite-volume scheme for conservation laws with a source term. Third-order accuracy is demonstrated for regular and irregular triangular grids for the linear advection and Burgers’ equations with a source term.     

Singular Limit of a Reaction-Diffusion Equation with a Spatially Inhomogeneous Reaction Term

We study reaction-diffusion equations with a spatially inhomogeneous reaction term. If the coefficient of these reaction term is much larger than the diffusion coefficient, a sharp interface appears between two different phases. We show that the equation of motion of such an interface involves a drift term despite the absence of drift in the original diffusion equations. In particular, we show that the same rich spatial patterns observed for a chemotaxis-growth model can be realized by a system without a drift term.     

Evaluation of the single ionisation transition amplitude using the CDW-EIS model within the framework of the impact-parameter method

The continuum distorted-wave model with an eikonal initial state for ionisation is discussed within the framework of the impact-parameter method. Particular attention is paid to the surface term, which describes the transition by a distorting potential, and which has been omitted in all of the previous calculations performed using the model. However, this term is included in the transition amplitude in a recent application of the model based upon a quantum-mechanical treatment. The present study, in which the surface term is evaluated within the impact-parameter method, shows that this term does not contribute to the transition amplitude. In describing the electron-ejection mechanism for a p^±–H collision, the cross-sections evaluated using the impact-parameter model show numerical agreement with those determined in the quantum-mechanical version. This agreement indicates that the contribution of the surface term calculated in the wave treatment is negligible over the region in which the impact-parameter model is valid.     

Perturbation theory and renormalization of supersymmetric Yang-Mills theories

We solve the problem of introducing, in supersymmetric Yang-Mills Lagrangians, a supersymmetric gauge breaking term and a Faddeev-Popov ghost interaction term. The resulting Lagrangian turns out to be invariant under a global symmetry transformation which is the supersymmetric extension of the Slavnov symmetry. We show that the complete analysis of all primitively divergent supergraphs ensures, in conjunction with the Slavnov identities, the renormalizability of the theory, once a supersymmetric and gauge invariant regularizing procedure has been introduced. We find that the simplest regularizing procedure is a generalization of the higher covariant derivatives method. In the case of interaction with matter fields we prove that no mass counter term is needed, in exact analogy with the model without gauge fields. Finally we show that, in the Abelian situation, a supersymmetric mass term for the vector multiplet can be introduced without spoiling the renormalizability, thus providing the supersymmetric extension of massive vector bosons theories.     

Locally Rotationally Symmetric Bianchi Type-I Model with Time Varying Λ Term

We investigate the locally rotationally symmetric (LRS) Bianchi type-I cosmological model for stiff matter and a vacuum solution with a cosmological term proportional to R^-m (R is the scale factor and m is a positive constant). The cosmological term decreases with time. We obtain that for both the cases the present universe is accelerating with a large fraction of cosmological density in the form of a cosmological term.     

Interrogating the Legend of Einstein's “Biggest Blunder”

It is well known that, following the emergence of the first evidence for an expanding universe, Albert Einstein banished the cosmological constant term from his cosmology. Indeed, he is reputed to have labelled the term, originally introduced to the field equations of general relativity in 1917 in order to predict a static universe, his “biggest blunder.” However, serious doubts about this reported statement have been raised in recent years. We interrogate the legend of Einstein’s “biggest blunder” statement in the context of our recent studies of Einstein’s cosmology in his later years. We find that the remark is highly compatible with Einstein’s cosmic models of the 1930s, with his later writings on cosmology, and with independent reports by at least three physicists. We conclude that there is little doubt that Einstein came to view the introduction of the cosmological constant term as a serious error and that he very likely labelled the term his “biggest blunder” on at least one occasion. This finding may be of some relevance for those theoreticians today who seek to describe the recently discovered acceleration in cosmic expansion without the use of a cosmological constant term.     

Dust Alfven ordinary and cusp solitons and modulational instability in a self-gravitating magneto-radiative plasma

The effective one-fluid adiabatic magnetohydrodynamic (MHD) equations for a multicomponent plasma comprising of electrons, ions, and dust are used to investigate the nonlinear coupling of dust Alfven and dust acoustic waves in the presence of radiation pressure as well as the Jean’s term that arises in a self-gravitating plasma. In this context, the set of Zakharov equations are derived. The soliton solutions in the presence of radiation pressure and Jeans term are separately discussed. It is found that ordinary solitons are obtained in the absence of Jeans term whereas cusp solitons are found in the absence of radiation pressure. To the best of our knowledge, cusp solitons are obtained for the first time for a self-gravitating plasma with Jeans term for an electromagnetic wave in a dusty plasma. The modulational instability is also investigated in the presence of radiation pressure and Jeans term. It is found that the Jeans term drives the system modulationally unstable provided it dominates the dust acoustic and radiation pressure terms whereas the radiation pressure enhances the stability of the system. The relevance of the present investigation in the photodissociation region that separates the HII region from the dense molecular clouds is also pointed out.     

Supergravity,R invariance and spontaneous supersymmetry breaking

We show that in order for a U(1) gauge theory with a Fayet-Illiopoulos term to be consistently coupled to supergravity, preserving gauge invariance, the superpotential must be R invariant. A supersymmetric cosmological term and therefore an explicit mass-like term for the gravitino is forbidden by gauge invariance. This result severely constrains the possible models for non-gravitational interactions. We comment on possible mass term the gauginos induced by gravitational effects.     

Off-shell corrections to the glauber theory of nuclear multiple scattering

We study the first-order off-shell corrections to Glauber's multiple scattering model. These consist of a direct and a rescattering term, and are obtained from the eikonal corrections studied in a previous paper by a simple substitution. For an independent particle nuclear model the direct term becomes identical to an expression previously derived by Moniz. We show that the rescattering term is in general not small compared to the direct term. For high incident energy a comparison is made with other corrections to the Glauber model. An optical potential is proposed which consists of the Glauber potential and its off-shell, eikonal, Fresnel and spatial correlation corrections.     

The long-range dependence behavior of the term structure of interest rates in Japan

This paper presents an empirical evidence suggesting that Japanese interest rates for different maturities possess long-range dependence in both mean and volatility. For long-term bonds, predictability in the term structure of interest rates increases with maturity, suggesting that there exists a term premium. Furthermore, the dynamics of short-term interest rates (6 months) is very different from longer term bonds, as the former are anti-persistent, which implies that the zero-interest rate policy is perceived to be temporary.     

A new traffic model with a lane-changing viscosity term

In this paper, a new continuum traffic flow model is proposed, with a lane-changing source term in the continuity equation and a lane-changing viscosity term in the acceleration equation. Based on previous literature, the source term addresses the impact of speed difference and density difference between adjacent lanes, which provides better precision for free lane-changing simulation; the viscosity term turns lane-changing behavior to a "force" that may influence speed distribution. Using a flux-splitting scheme for the model discretization, two cases are investigated numerically. The case under a homogeneous initial condition shows that the numerical results by our model agree well with the analytical ones; the case with a small initial disturbance shows that our model can simulate the evolution of perturbation, including propagation,dissipation, cluster effect and stop-and-go phenomenon.     

Radiation-spin interaction, Gilbert damping, and spin torque

Magnetization relaxation processes, which are represented by the Gilbert damping term and the spin torque term in the Landau-Lifshitz-Gilbert (LLG) equation, are described by the radiation-spin interaction (RSI), where the radiation field is produced by magnetization precessional motion itself. It is shown that the LLG equation including the Gilbert damping term and the spin torque term is derived from the spin Hamiltonian containing the RSI. The derivation of the LLG equation is given in a self-consistent method. It is also shown that, according to RSI, the magnitude of the magnetization vector deviates from the magnetization saturation with the order of O(alpha(2)), where alpha is the Gilbert damping parameter.     

Continuous phase transitions which should be first order

It is demonstrated that phase transitions predicted to be first order by the Landau symmetry arguments can be continuous for a finite range of the physical parameters. For transitions with a rank-two tensor order parameter it is shown that fluctuations in a phase associated with the anisotropy of the tensor result in a renormalization of the cubic term. This leads to continuous transitions when the coefficient of the bare cubic term is small compared to the coefficient of the quartic term. It is shown that the argument can be extended to more general cases when the order parameter belongs to a multidimensional representation of the broken symmetry group.     

Cosmologies based on Lyra's geometry

It is pointed out that the cosmologies based on Lyra's manifold, with constant gauge-vector which have been studied in the literature, will either include a creation field and be equal to Hoyle's creation field cosmology, or contain a special vacuum fluid which together with the gauge-vector term may be considered as a cosmological term. In the latter case the solutions are equal to the general relativistic cosmologies with a cosmological term.