Generalized Dirichlet Normal Ordering in Open Bosonic Strings

Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.     

Effect of stress state on deformation and fracture of nanocrystalline copper:Molecular dynamics simulation

Deformation in a microcomponent is often constrained by surrounding joined material making the component under mixed loading and multiple stress states. In this study, molecular dynamics(MD) simulation are conducted to probe the effect of stress states on the deformation and fracture of nanocrystalline Cu. Tensile strain is applied on a Cu single crystal,bicrystal and polycrystal respectively, under two different tension boundary conditions. Simulations are first conducted on the bicrystal and polycrystal models without lattice imperfection. The results reveal that, compared with the performance of simulation models under free boundary condition, the transverse stress caused by the constrained boundary condition leads to a much higher tensile stress and can severely limit the plastic deformation, which in return promotes cleavage fracture in the model. Simulations are then performed on Cu single crystal and polycrystal with an initial crack. Under constrained boundary condition, the crack tip propagates rapidly in the single crystal in a cleavage manner while the crack becomes blunting and extends along the grain boundaries in the polycrystal. Under free boundary condition, massive dislocation activities dominate the deformation mechanisms and the crack plays a little role in both single crystals and polycrystals.     

Regular Charged Solutions in Mφller＇s Tetrad Theory of Gravitation

We find the most general tetrads which give a regular charged spacetime in tetrad theory of gravitation. The metric is a static one and it includes the Schwarzschild and Fteissner Nordstrom black holes. The energy content contained in a sphere of radius R is calculated using the superpotential given by Mφller in the context of Weitzenbock spacetime.     

Bosonic and Fermionic Entropy of (2 1)-Dimensional Charged Black Hole

From resolving Klein-Gordon equation and Dirac equation in (2 1)-dimensional charged black hole spacetime and using ‘t Hooft‘s boundary condition and “quasi-periodic“ boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2 1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.     

Adiabatic regularization and Green's function of a scalar field in de Sitter space: Positive energy spectrum and no trace anomaly

In the conventional adiabatic regularization the vacuum ultraviolet divergences of a quantum field in curved spacetime are removed by subtracting the k-mode of the stress tensor to the 4 th-order.For a scalar field in de Sitter space,we find that the4 th-order regularized spectral energy density is negative.Moreover,the 2 nd-order regularization for minimal coupling(ξ=0)and the 0 th-order regularization for conformal coupling(ξ=1/6) yield a positive and UV-convergent spectral energy density and power spectrum.The regularized stress tensor in the vacuum is maximally symmetric and can drive inflation,while its k-modes representing the primordial fluctuations are nonuniformly distributed.Conventional regularization of a Green's function in position space is generally plagued by a log IR divergence.Only in the massless case with ξ=0 or 1/6,we can directly regularize the Green's functions and obtain vanishing results that agree with the adiabatic regularization results.In this case,the regularized power spectrum and stress tensor are both zero,and no trace anomaly exists.To overcome the log IR divergence problem in the massive cases with ξ=0 and 1/6,we perform Fourier transformation of the regularized power spectra and obtain the regularized analytical Green's functions which are IR-and UV-convergent.     

Tensor Fields on Self-Dual Warped AdS_3 Background

Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3-dimensional self-dual space-like warped AdS_3 black hole background. We obtain a Klein–Gordon-like equation for tensor fields. By using gauge constraint and traceless condition, we will find the exact solutions of the equations of motion. Then, we will compute the quasi-normal modes by imposing appropriate boundary conditions at horizon and infinity.     

Quadrupole-octopole alignment of CMB related to the primordial power spectrum with dipolar modulation in anisotropic spacetime

The WMAP and Planck observations show that the quadrupole and octopole orientations of the CMB might align with each other. We reveal that the quadrupole-octopole alignment is a natural implication of the primordial power spectrum in an anisotropic spacetime. The primordial power spectrum is presented with a dipolar modulation. We obtain the privileged plane by employing the “power tensor” technique. At this plane, there is maximum correlation between quadrupole and octopole. The probability for the alignment is much larger than that in the isotropic universe. We find that this model would lead to deviations from the statistical isotropy only for low-l multipoles.     

Surface Gravity on the Horizon of η- ξ Spacetime

We investigate the two methods of defining the surface gravity ,κ on the horizon, which are the metric definition and the definition given by the spacetime conformal method. It is found that the latter is of greater generality. By this method, we find that ,κ of η- ξ spacetime is equal to the exponent factor α in the coordinate transformation, which confirms the argument that η- ξ spacetime can be considered as the background spacetime for finitetemperature field theories. The reasons why the metric definition of ,κ can not be applied in η- ξ spacetime are presented.     

Tachyon Vortex

The properties and gravitational fields of global strings of tachyon matter are investigated in four-dimensional approximately cylindrically symmetric spacetime with a deficit angle. In particular, we give an exact solution of the tachyon field in the fiat spacetime background and we also find the solution of the metric in the linearized approximation of gravity.     

Applications of the Junction Conditions Connecting the Robertson-Walker Metric and the Metric of a Local System on Our Universe

We investigate how the local and global metrics are connected in an ideal model of spacetime where the local system is assumed to be highly symmetric and the cosmological matter is kept away from the local system and does not disturbed by the local system. A boundary condition arising from the junction conditions is obtained and its implication in our universe is studied. We know that the total mass of a sufficiently large system must be that of the cosmological matter within the region of that size. This requirement is satisfied since it is just a consequence of the boundary condition. The analysis shows that at the very late epoch of the universe, there exists a particular time when the largest symmetric local systems stop growing and the observation of this time can be used to check the cosmological parameters. Adopting the popular values （ΩM, Ωa） = （0.28, 0.72）, we find that particular time would be associated with z = 0.726, the effect of dark matter on the clustering of objects would be insignificant, and the Virgo cluster would be gravitationally bound even if dark matter is ignored.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both flat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimir effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet ard Neumann boundary conditions are also discussed.     

Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.     

Existence of maximal surfaces in asymptotically flat spacetimes

We prove the existence of maximal surfaces in asymptotically flat spacetime satisfying an interior condition. This uses a priori estimates which can also be applied to prescribed mean curvature surfaces in cosmological spacetimes and the Dirichlet problem.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables X ^μ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.     

二维静态时空中Dirac场的重正化能动张量和Casimir效应

在一般渐近平直的二维静态黑洞时空中,利用重正化能动张量的一般性质, 对位于两“平行板”间满足Dirichlet条件的无质量Dirac场的重正化能动张量的真空期待值进行了分析和计算, 得到了一般表达式.利用该表达式可以给出各种具体渐近平直二维静态黑洞时空中的相应Casimir力.对于重正化能动张量及Casimir力与真空态定义(包括Boulware 真空态、Hartle-Hawking真空态和Unrum真空态三种情况)、Hawking辐射和反常迹的关系分别进行了讨论，给出了相应的表达式和计算结果. 关键词： 能动张量 Casimir 效应 黑洞 真空态     

On open boundary conditions for long wave equation in the hodograph plane

We discuss implications of the seaward boundary conditions used in initial-boundary value problem formulation of nonlinear shallow-water wave propagation over a linear slope. We first demonstrate the reflection of wave velocity in the case of Dirichlet condition and that of water elevation in the case of Neumann condition. We then show that linear superposition of the two boundary conditions results in much less reflection at the artificial boundary. We also propose a new boundary condition of mixed type and compare its results with that of the aforementioned conditions.     

Instability of flat spacetime in semiclassical gravity

The semiclassical theory of gravity is considered in which an asymptotically flat background metric is coupled to quantized matter. We show that, in general, there are modes with spacelike wave vectors for small metric fluctuations around flat spacetime. Besides the usual axioms of quantum field theory in flat spacetime, the proof rests on the existence of a hard trace anomaly in the energy-momentum tensor due to matter self-couplings. Two possible interpretations of the result are discussed.