A reformulation of the one-dimensional surface field integral equations

By starting from the matrix forms of the two coupled, inhomogeneous integral equations for the values of the magnetic field and its normal derivative on a one-dimensional, rough metal surface, or for the values of the electric field and its normal derivative on such a surface, we have obtained an equivalent pair of equations for these quantities in which the inhomogeneous terms are just the Kirchhoff approximations to them. The new pair of equations for the surface values of the magnetic field and its normal derivative is solved iteratively to generate a multiple-scattering expansion for the scattering amplitude when p-polarized light is scattered from a large RMS height, large RMS slope, one-dimensional, random silver surface, with the plane of incidence perpendicular to the generators of the surface. It is shown that the Kirchhoff approximation to the contribution to the mean differential reflection coefficient from the incoherent component of the scattered light displays no evidence of enhanced backscattering. However, the pure double-scattering contribution already displays this effect, stamping it as a multiple-scattering phenomenon.     

Non-perturbative renormalization group calculation of the scalar self-energy

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.     

Power-Law Expansion and Scalar Field Cosmology in Higher Derivative Theory

In this paper we study the evolution of a flat Friedmann-Robertson-Walker model filled with a perfect fluid and a scalar field minimally coupled to gravity in higher derivative theory of gravitation. Exact solution of the field equations are obtained by the assumption of power-law form of the scale factor. A number of evolutionary phases of the universe including the present accelerating phase are found to exist with scalar field in the higher derivative theory of gravitation. The properties of scalar field and other physical parameters are discussed in detail. We find that the equation of state parameter for matter and scalar field are same at late time in each case. We observe that a higher derivative term can hardly be a candidate to describe the presently observed accelerated expansion. It is only the hypothetical fluids, which provide the late time acceleration. It is also remarkable that the higher derivative theory does not effect the radiating model of scalar field cosmology.     

A reformulation of the one-dimensional surface field integral equations

Abstract

By starting from the matrix forms of the two coupled, inhomogeneous integral equations for the values of the magnetic field and its normal derivative on a one-dimensional, rough metal surface, or for the values of the electric field and its normal derivative on such a surface, we have obtained an equivalent pair of equations for these quantities in which the inhomogeneous terms are just the Kirchhoff approximations to them. The new pair of equations for the surface values of the magnetic field and its normal derivative is solved iteratively to generate a multiple-scattering expansion for the scattering amplitude when p-polarized light is scattered from a large RMS height, large RMS slope, one-dimensional, random silver surface, with the plane of incidence perpendicular to the generators of the surface. It is shown that the Kirchhoff approximation to the contribution to the mean differential reflection coefficient from the incoherent component of the scattered light displays no evidence of enhanced backscattering. However, the pure double-scattering contribution already displays this effect, stamping it as a multiple-scattering phenomenon.     

Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres’ theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres’ theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.     

Gravitation,torsion, and electromagnetism

A term bilinear in the derivative of the torsion is added to the Lagrangian of general relativity to produce torsion that propagates. Using standard variational techniques, field equations are derived with the torsion being interpreted as the electromagnetic potential and the antisymmetric part of the Ricci tensor as the electromagnetic field tensor. The equation of motion is derived from the field equations, and the results are compared to the Einstein-Maxwell formulation.     

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.     

New exact solutions of the Einstein-Maxwell equations for magnetostatic fields

The symmetry reduction method based on the Fr′echet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.     

New exact solutions of Einstein—Maxwell equations for magnetostatic fields

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

Epsilon expansion for multicritical fixed points and exact renormalisation group equations

The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its extension, the derivative expansion. The results are compared with the epsilon expansion by showing that the nonlinear differential equations may be linearised at each multicritical point and the epsilon expansion treated as a perturbative expansion. The results for critical exponents are compared with corresponding epsilon expansion results from standard perturbation theory. The results provide a test for the validity of the local potential approximation and also the derivative expansion. An alternative truncation of the exact RG equation leads to equations which are similar to those found in the derivative expansion but which gives correct results for critical exponents to order ε and also for the field anomalous dimension to order ε². An exact marginal operator for the full RG equations is also constructed.     

小孔衍射和近场散射数值计算的格林函数方法

从简谐光波满足的亥姆霍兹方程出发,将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组,并对其进行数值求解,实现了光场的数值计算。然后将这一方法应用于亚波长尺度的小孔衍射的光波以及自仿射分形表面产生的随机光场及其在近场区域范围内的传播的计算。在随机表面产生的光场计算中．提出了类比推导夫琅禾费面上散斑场自相关函数的方法产生随机表面,以及计算其导数的傅里叶变换方法。对光场的计算结果表明,在近场范围内,光场随离开表面的距离的增加而迅速变化,其传播特性完全不同于光场在远场范围内的传播特性。     

The generalized Einstein-Maxwell theory of gravitation

A new Lagrangian theory of gravitation in which the metric and the arbitrary affine connection are regarded as independent field variables has been considered. Making use of the pure geometrical objects only from the variational principle the empty field equations are derived. It is shown that the metric obeys the ordinary Einstein equations of general relativity. However, the covariant derivative of the metric tensor does not vanish, so that the vector's length is generally nonintegrable under the parallel displacement. The torsion trace vector turns out to be the natural dynamical variable, satisfying the Maxwell-like equations with tensor of homothetic curvature as the Maxwell tensor. The equations of motion are explored; they are shown to be identical to the motion of electric charge under the Lorentz force. The conservation laws are discussed.     

DERIVATION OF THE LEHNERT FIELD EQUATIONS FROM GAUGE THEORY IN VACUUM: SPACE CHARGE AND CURRENT

It is shown that the Lehnert field equations in vacuum, with concomitant space charge and current, can be derived straightforwardly from standard gauge theory applied in vacuum, using the concept of covariant derivative and Feynman's universal influence. The Lehnert and Proca field equations are shown to be inter-related through the well-known de Broglie theorem, in which the photon mass can be interpreted as finite. These ideas go some way towards addressing the inconsistency inherent in Maxwell's famous displacement current, which has no concomitant vacuum space charge.     

Symmetry classes ofpp-waves

The isometry groups admitted by plane-fronted gravitational waves with parallel rays are determined without use of any field equations. New groups with 5, 6, and 7 parameters arise which cannot occur for (nontrivial) exact solutions of Einstein's vacuum field equations. For all 17 possible cases the functional form of the free function in the metric is given. We apply the classification to Einstein-Maxwell fields and also determine, in Riemann-Cartan geometry, the form of the torsion tensor by assuming the vanishing of its Lie derivative with respect to the generators of the isometry groups.     

Completely integrable models of nonlinear optics

The models of the nonlinear optics in which solitons appeared are considered. These models are of paramount importance in studies of nonlinear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency and parametric interaction of three waves. At present there are a number of theories based on completely integrable systems of equations, which are, both, generations of the original known models and new ones. The modified Korteweg-de Vries equation, the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation. Sine-Gordon equation, the reduced Maxwell-Bloch equation. Hirota equation, the principal chiral field equations, and the equations of massive Thirring model are some soliton equations, which are usually to be found in nonlinear optics theory.     

Tetrad formulation of gravity with a torsion potential

A tetrad formulation of gravity with a torsion potential is presented. The torsion is derived from the exterior derivative of a second rank tensor potential. The geometrical Lagrangian is the curvature scalar and variations are taken with respect to the tetrad components. It is shown that the resulting field equations, and conservation laws, are identical to those obtained in a purely holonomic frame.     

双压电材料三维界面端部力电耦合场奇异性

基于切口根部物理场的幂级数渐近展开假设,从三维应力平衡方程和麦克斯韦方程组出发,导出关于双压电材料楔形界面切口端部奇性指数的特征微分方程组,并将切口的力电学边界条件表达为奇性指数和特征角函数的组合,从而将双压电材料楔形界面切口端部奇性指数的计算转化为相应边界条件下常微分方程组特征值的求解,运用插值矩阵法求解界面端部若干阶应力奇性指数和相应特征函数.计算结果与已有结果对比表明本文方法的有效性和具有较高的计算精度.     

Constraint equations for general hypersurfaces and applications to shells

Hypersurfaces of arbitrary causal character embedded in a spacetime are studied with the aim of extracting necessary and sufficient free data on the submanifold suitable for reconstructing the spacetime metric and its first derivative along the hypersurface. The constraint equations for hypersurfaces of arbitrary causal character are then computed explicitly in terms of this hypersurface data, thus providing a framework capable of unifying, and extending, the standard constraint equations in the spacelike and in the characteristic cases to the general situation. This may have interesting applications in well-posedness problems more general than those already treated in the literature. As a simple application of the constraint equations for general hypersurfaces, we derive the field equations for shells of matter when no restriction whatsoever on the causal character of the shell is imposed.