Thermal Squeezed State Representation of Scalar Field and Energy Density in Semiclassical Theory of Gravity

The semiclassical theory of gravity is studied in terms of representation of scalar field in thermal coherent state and thermal squeezed state formalisms. For the FRW cosmological model with a minimal scalar field, the semiclassical Einstein equation reduces to zero-point energy term plus a finite temperature term and classical term in thermal coherent state. In thermal squeezed vacuum state it reduces to quantum term in addition to the finite temperature term and zero-point energy term. The present study can account for nonclassical state and finite temperature effect contributions to energy density in semiclassical theory of gravity.     

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.     

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.     

Analytic vectorial structure of circular flattened Gaussian beams

By means of the method of vector angular spectrum representation and the mathematical techniques, the analytically vectorial structure of the circular flattened Gaussian beam (CFGB) is derived without any approximation, which can be applicable to an arbitrary observation plane. In the far-field, the analytical formulae of the TE and the TM terms are further simplified using the method of stationary phase. The analytical expressions of the energy flux for the TE term, the TM term, and the CFGB are also presented. The energy flux distributions of the TE term, the TM term, and the CFGB are demonstrated in different reference planes, and the evolvement of the patterns of the TE term, the TM term, and the CFGB upon propagation are graphically illustrated.     

Vectorial structure of the far-field of an apertured four-petal Gaussian beam

Based on the theorem of vectorial structure and the method of stationary phase, an analytical vectorial structure of the far-field of an apertured four-petal Gaussian beam has been derived without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured four-petal Gaussian beam are also presented in the far-field reference plane, respectively. The energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam are graphically demonstrated in the far-field plane. The dependences of the energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam on the f-parameter, the truncation parameter, and the beam order are also examined.     

The Three Avtars of the Chern-Simons Term in 3 Space-Time Dimensions

I discuss in detail the three “avtars” of the Chern-Simons (C-S) term in 2 + 1 dimensions i.e. (i) C-S term as gauge field mass term (ii) C-S term as a purely kinematic term (iii) gauge theories with purely C-S action. In the first case we find that because of the C-S term one has massive gauge quanta and still the theory is gauge invariant. Such a C-S term can be generated either by spontaneous symmetry breaking or by radiative corrections. The dramatic effect of this term is that the vortices of the abelian (or nonabelian) Higgs model now have finite, quantized charge and angular momentum. In the second case the C-S term is not really independent but can be expressed in terms of the basic quanta of the 0(3) nonlinear σ-model or CP¹ model. In either case one finds that due to this term the soliton of the model has fractional spin and statistic interpolating between fermions and bosons. The relevance of this in the context of high-T_c, superconductivity is discussed in some detail. Finally the third avtar has to do with some recent work of Witten where he has shown that the Hilbert spaces of the quantum Yang-Mills theory with pure C-S action can be interpreted as the spaces of the conformal blocks in 1 + 1 dimensional conformal theories.     

The Pietra term structures of financial assets

This paper explores an elemental connection between call options-the most commonly tradable financial derivatives, implied volatility term structures-critical “market information” emanating from call-option prices, and the Pietra index-a quantitative economic measure of societal egalitarianism. Our study: (i) unveils an intrinsic “Pietra structure” of call-option prices; (ii) introduces the notion of the “Pietra term structures” of financial assets; (iii) describes the probabilistic meaning of the Pietra term structures; (iv) establishes an explicit nonlinear one-to-one mapping between the Pietra term structures and the implied volatility term structures of financial assets. The results presented in this paper provide a deep insight into the econophysics of call options and implied volatility term structures.     

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.     

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.     

Analytically vectorial structure of an apertured Laguerre-Gaussian beam in the far-field

Based on the angular spectrum representation of an arbitrary electromagnetic beam and the method of stationary phase, an analytically vectorial structure of an apertured Laguerre-Gaussian beam in the far-field has been derived without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured Laguerre-Gaussian beam are also presented in the far-field, respectively. The energy flux distributions of the TE term, the TM term, and the apertured Laguerre-Gaussian beam are numerically demonstrated in the far-field reference plane. The influences of the f-parameter, the truncation parameter, the radial and angular mode numbers, and the dependent relation of angle on the energy flux distributions in the far-field of the TE term, the TM term, and the apertured Laguerre-Gaussian beam are also discussed in detail.     

Pregeometrical string field theory: Creation of space-time and motion

A space-time-metric-independent and gauge-invariant formulation of closed-string field theory is proposed. The action contains no kinetic term and consists solely of a cubic term in the string field. The kinetic term can be generated through the condensation of an infinitesimally small string.     

Holonomy and the Wess-Zumino term

The concept of a holonomy term in a Lagrangian is introduced. It unifies the idea of the interaction term in the Dirac monopole and the Wess-Zumino term. In particular, it provides a dynamical interpretation of the Kac-Moody cocycle on a loop group.     

Fractional spin and the Pauli term

It has recently been claimed that the inclusion of a Pauli term in (2+1) dimensions gives rise to a new type of anomalous spin term. The form of that term is shown to contradict the structure relations for the inhomogeneous Lorentz group.     

一种数字全息图零级项消除的新方法

针对离轴数字全息图中的零级项问题,提出用独立分量分析方法对零级项进行压缩.首先通过CCD获取同一物体的两幅干涉强度不同的全息图构成观测信号,然后采用独立分量分析方法(Independent Component Analysis(ICA))从观测信号中分离出零级项和共轭项,再从获得的共轭项中减去残余的零级项分量,实现零级项的有效压缩,并用模拟结果论证该方法在处理零级项压缩方面的优越性和有效性.     

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.     

Induced Chern-Simons term of a paired electron state in the quantum Hall system

The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the usual term proportional to a filling factor due to P (parity) & T (time reversal) symmetry breaking but also correction terms due to P & T & U(1) symmetry breaking. The correction term essentially comes from the Nambu-Goldstone mode and depends on an infrared limit. It is shown that the correction term is related to a topological number of a gap function in the momentum space.     

各向同性光波导受到各向同性微扰时的严格矢量耦合模理论

从Maxwell方程出发,推导出各向同性光波导受到各向同性微扰时严格的非正交矢量耦合模理论,在耦合系数的表达式中发现不包含Wei-Ping Huang 的准矢量耦合模理论中的偏振耦合项,但在推导过程中曾出现过偏振耦合项.最后认为这是由于偏振耦合项是二阶小量,而弱导近似忽略了与之相等的二阶小量耦合项.因此,严格的矢量耦合模理论不存在该项而准矢量耦合模理论可把偏振耦合项作为修正项.     

On the nielsen-taylor effect in the diffusion thermopower of dilute alloys

It is suggested that the electron-phonon vertex correction to the electron-impurity scattering gives rise to an additional term in the diffusion thermopower of dilute alloys at low temperatures. The absolute magnitude of the additional term is similar to the Nielsen-Taylor term. The experiment which can detect these effects is investigated.     

CP~1模型的拓扑项的可移性与θ真空

研究了１十１维ＣＰ１模型的拓扑项的可移性，求得了移去ＣＰ１模型拓扑项的么正变换，并且找到了拓扑项与　真空以及几何相因子的关系．     

Residual resistivity dipoles in electromigration

In the presence of an electric field a driving force is exerted by the surrounding electron gas on the impurity atoms. The contribution from this term is usually referred to as the Bosvieux-Friedel term who related it to the residual resistivity of the impurity. It has been suggested that the residual resistivity of the impurity causes a dipolar buildup around the impurity resulting in the so-called residual resistivity dipoles (RRD's) which in turn contribute a term to the driving force, in addition to the Boxvieux-Friedel term. We discuss the nature of this term for an impurity in a jellium matrix using nonlinear screening theory. It is found to vanish if it is identified with the third order terms in the impurity potential representing contribution from the RRD's.