Kalb–Ramond fields and the CMBR

Cosmological implications on the polarization of the cosmic microwave background radiation, of a Kalb–Ramond field interacting with gauge fields and gravity as dictated by quantum consistency of heterotic string theory are surveyed. A parity violating augmentation going beyond the dictates of string theory is shown to lead to possible appearance of a B mode generated in the cosmic microwave background (CMB) in the post-last scattering epoch. This generation of the B mode of CMB appears to be dramatic when the augmentation is embedded within a Randall–Sundrum braneworld scenario of the first kind.     

Invariant Solutions of the Yang–Mills Field Equations Coupled to a Scalar Doublet

The Yang–Mills system of field equations which includes coupling to an SU(2) scalar matter doublet is developed. It is shown that an SU(2) current for a scalar matter doublet can be developed. The basic structure which fits the Yang–Mills system is somewhat different from the case of the scalar triplet. Using this form for the scalar current, it is possible to write down the Yang–Mills system which couples to the scalar matter doublet. It is shown that several sets of solutions to this system of equations can be obtained.     

On a Unified Theory of Generalized Branes Coupled to Gauge Fields,Including the Gravitational and Kalb–Ramond Fields

We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates and associated coordinate frame fields {} extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The “extra dimensions” are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb–Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe–Tucker action in curved C-space.     

Generalized Rashba Coupling Approximation to a Resonant Spin Hall Effect of the Spin–Orbit Coupling System in a Magnetic Field

We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field. A solvable Hamiltonian is obtained by performing a simple change of basis, which has the same form as that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state. Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting, exhibiting the validity of the analytical approximation. By using the eigenstates, spin polarization correctly displays a jump at the energy-level crossing point, where the corresponding spin conductance exhibits a pronounced resonant peak. As the component of the Dresselhaus coupling increases,the resonant point shifts to a smaller value of the magnetic field. In contrast to pure Rashba couplings, we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.     

Dynamical Evolution of a Scalar Field Coupling to Einstein’s Tensor in Charged Braneworld Black Holes

In this work, we study the quasinormal modes (QNMs) of scalar field coupling to Einstein’s tensor in charged braneworld black hole. The shape of the potential function is illustrated and we find that lower coupling constant leads to more stable field. We then apply six-order WKB approximation to calculate the quasinormal frequencies (QNF) in weaker coupling field, and depict the dependence of the oscillation frequency on the coupling constant. Furthermore, we use finite difference method to shape the evolution of the coupling field and find that coupling field with lower multipole numbers l corresponds to stable field, while higher l tends to lead to instability when the coupling constant is larger than a threshold value. Finally the fitting curve of such threshold value is given numerically.     

Direction Finding with a Vector–Scalar Receiver in the Field of Anisotropic Interference

Acoustical Physics - A mathematical model of an anisotropic acoustic field is constructed based on the multidimensional Poisson process. The relationship between the probabilistic characteristics...     

Radiative Energy Shifts of an Accelerated Multilevel Atom Coupled to the Derivative of a Scalar Field

We study the energy level shifts of an accelerated multilevel atom in dipole coupling to the derivative of a quantum massless scalar field and separately calculate the contributions of vacuum fluctuations and radiation reaction to the shifts. It is found that, in contrast to the case of a monopole-like interaction, both the vacuum fluctuations and radiation reaction contributions are changed by acceleration, and they all contain non-thermal correction terms. Our results suggest that the effect of acceleration on the energy shifts is dependent on the type of the interaction between the atom and the quantum field.     

Quasinormal Modes of a Coupled Scalar Field in the Acoustic Black Hole Spacetime

By using the third-order Wentzel-Kramers-Brillouin approximation and the monodromy methods, the quasnormal modes of a coupled scalar field in the canonical non-rotating acoustic black hole spacetime are investigated. It is shown that the coupling between the scalar field and background metric affects the quasinormal frequencies. At low overtones, both the real part and the magnitude of imaginary part increase with the couple factor ξ. For the larger ξ, both of them are almost linearly related to the couple factor. At high overtones, it is found that the frequency formula of the quasinormal modes is 2πω/κ = ln （ 1 ＋ 2 cos√9-24ξ/5 π） - i（2n ＋ 1）π, which means that 5 when ξ is larger, the real part is the linear function of ξ^1/2.     

Dark Energy Model with Canonical Scalar Field and Non-Linear Born–Infeld Type Scalar Field

In this paper, we propose the non-linear Born–Infeld scalar field and canonical scalar field dark energy models with the potential , which admits late time de Sitter attractor solution. The attractor solution corresponds to an equation of state ω_φ → − 1 and a cosmic density parameter Ω_φ → 1, which are important features for a dark energy model that can meet the current observations. dark energy; canonical scalar field, non-linear Born–Infeld type scalar field, attractor solution. PACS number(s):98.80.-k; 98.80.Cq; 98.80.Es.     

Scalar Field at the Phase Transition Point of RNdS Space

The real scalar field equation between the outer black hole horizon and the cosmological horizon is solved in the Reissner-Nordstroem-de Sitter space when it is at the phase transition point. We use an accurate approximation,the polynomial approximation, to approximate the tortoise coordinate x(r) for obtaining the inverse function r=r(x) and then for solving the wave equation. The case where the two horizons are very close to each other is discussed in detail. It is found that the wave function is characteristically similar to the harmonic in the whole range with x as the independent coordinate, while the waves pile up near the horizons with r as the independent coordinate. Furthermore, we find that the height of the potential increases as the cosmological constant A decreases.     

A comment on discrete Kalb–Ramond field on orientifold and rank reduction

We show that the rank reduction of the gauge group on orientifolds in presence of non-vanishing discrete Kalb–Ramond field can be explained by the presence of an induced field strength in a non-trivial bundle on the branes. This field strength is also necessary for the tadpole cancellation and the number of branes is left unchanged by the presence of the discrete Kalb–Ramond background. We moreover give a derivation of the normalization of the Möbius amplitude in presence of a non-vanishing Kalb–Ramond field from first principles.     

Quintessence Cosmology with a Coupled Real Scalar Field

In the light of the recent observations of type Ia supernovae (SNe Ia) suggesting an accelerating Universe,we show the possibility of a coupled real scalar field to be quintessence for the source of the accelerating Universe.We derive the main equations which govern the evolution of the Universe and rewrite them with the observable quantities.Finally we point out very briefly how future observations may determine the equation of state of quintessence.     

LETTER: On the Minimal Angular Size in Open, ΛCDM, and Scalar Field Cosmologies

We propose a simple method for determining the redshift z _m at which the angular size of an extragalactic source with fixed proper diameter takes its minimal value. A closed analytical expression, which is often convenient for numerical evaluation is derived. The method is exemplified with the following FRW type expanding universes: the open matter dominated models ( = 0), a critical density model with cosmological constant ( 0), and the class of scalar field cosmologies proposed by Ratra and Peebles. The influence of systematic evolutionary effects is briefly discussed.     

Two-Dimensional Klein–Gordon Oscillator in the Presence of a Minimal Length

Minimal length of a two-dimensional Klein–Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The eigensolutions are found and the system is mapping to the wellknown Schrödinger equation in a Pöschl–Teller potential.     

Vacuum Stability of the Wrong Sign (−ϕ 6) Scalar Field Theory

We apply the effective potential method to study the vacuum stability of the bounded from above (?? ⁶) (unstable) quantum field potential. The stability (?E/?b = 0) and the mass renormalization (? ² E/?b ² = M ²) conditions force the effective potential of this theory to be bounded from below (stable). Since bounded from below potentials are always associated with localized wave functions, the algorithm we use replaces the boundary condition applied to the wave functions in the complex contour method by two stability conditions on the effective potential obtained. To test the validity of our calculations, we show that our variational predictions can reproduce exactly the results in the literature for the \(\mathcal {PT}\) -symmetric ? ⁴ theory. We then extend the applications of the algorithm to the unstudied stability problem of the bounded from above (?? ⁶) scalar field theory where classical analysis prohibits the existence of a stable spectrum. Concerning this, we calculated the effective potential up to first order in the couplings in d space-time dimensions. We find that a Hermitian effective theory is instable while a non-Hermitian but \(\mathcal {PT}\) -symmetric effective theory characterized by a pure imaginary vacuum condensate is stable (bounded from below) which is against the classical predictions of the instability of the theory. We assert that the work presented here represents the first calculations that advocates the stability of the (?? ⁶) scalar potential.     

Scalar Field Model of Dark Energy In the Double Complex Symmetric Gravitational Theory

The scalar field model of dark energy is established in the double complex symmetric gravitational theory. The universe we live in is taken as the real part of double complex space M^4C（J）. The two cases of scalar field （ordinary and phantom scalar field） are discussed in a unified way. Not only can the double Friedmann equations be obtained, but also the equation of state for dark energy, potential V（φ） and scalar field φ can be expressed. Hence, a new method is proposed to study dark energy and the evolution of the universe.     

Coupling of Two Conformal Field Theories and Nakajima–Yoshioka Blow-Up Equations

We study the conformal vertex algebras which naturally arise in relation to the Nakajima–Yoshioka blow-up equations.