Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.     

广义量子干涉原理及对偶量子计算机

我们综述最近提出的广义量子干涉原理及其在量子计算中的应用。广义量子干涉原理是对狄拉克单光子干涉原理的具体化和多光子推广,不但对像原子这样的紧致的量子力学体系适用,而且适用于几个独立的光子这样的松散量子体系。利用广义量子干涉原理,许多引起争议的问题都可以得到合理的解释,例如两个以上的单光子的干涉等问题。从广义量子干涉原理来看双光子或者多光子的干涉就是双光子和双光子自身的干涉,多光子和多光子自身的干涉。广义量子干涉原理可以利用多组分量子力学体系的广义Feynman积分表示,可以定量地计算。基于这个原理我们提出了一种新的计算机,波粒二象计算机,又称为对偶计算机。在原理上对偶计算机超越了经典的计算机和现有的量子计算机。在对偶计算机中,计算机的波函数被分成若干个子波并使其通过不同的路径,在这些路径上进行不同的量子计算门操作,而后这些子波重新合并产生干涉从而给出计算结果。除了量子计算机具有的量子平行性外,对偶计算机还具有对偶平行性。形象地说,对偶计算机是一台通过多狭缝的运动着的量子计算机,在不同的狭缝进行不同的量子操作,实现对偶平行性。目前已经建立起严格的对偶量子计算机的数学理论,为今后的进一步发展打下了基础。本文着重从物理的角度去综述广义量子干涉原理和对偶计算机。现在的研究已经证明,一台d狭缝的n比特的对偶计算机等同与一个n比特+一个d比特(qudit)的普通量子计算机,证明了对偶计算机具有比量子计算机更强大的能力。这样,我们可以使用一台具有n+log2d个比特的普通量子计算机去模拟一个d狭缝的n比特对偶计算机,省去了研制运动量子计算机的巨大的技术上的障碍。我们把这种量子计算机的运行模式称为对偶计算模式,或简称为对偶模式。利用这一联系反过来可以帮助我们理解广义量子干涉原理,因为在量子计算机中一切计算都是普通的量子力学所允许的量子操作,因此广义量子干涉原理就是普通的量子力学体系所允许的原理,而这个原理只是是在多体量子力学体系中才会表现出来。对偶计算机是一种新式的计算机,里面有许多问题期待研究和发展,同时也充满了机会。在对偶计算机中,除了幺正操作外,还可以允许非幺正操作,几乎包括我们可以想到的任何操作,我们称之为对偶门操作或者广义量子门操作。目前这已经引起了数学家的注意,并给出了广义量子门操作的一些数学性质。此外,利用量子计算机和对偶计算机的联系,可以将许多经典计算机的算法移植到量子计算机中,经过改造成为量子算法。由于对偶计算机中的演化是非幺正的,对偶量子计算机将可能在开放量子力学的体系的研究中起到重要的作用。     

String Cosmological Solutions with O(d,d) Duality Symmetry and Matter Coupling

The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.     

Wave mechanics and general relativity: a rapprochement

Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.     

An indirect approach for quantum-mechanical eigenproblems: duality transforms

We suggest an indirect approach for solving eigenproblems in quantum mechanics. Unlike the usual method, this method is not a technique for solving differential equations. There exists a duality among potentials in quantum mechanics. The first example is the Newton–Hooke duality revealed by Newton in Principia. Potentials that are dual to each other form a duality family consisting of infinite numbers of family members. If one potential in a duality family is solved, the solutions of all other potentials in the family can be obtained by duality transforms. Instead of directly solving the eigenequation of a given potential, we turn to solve one of its dual potentials which is easier to solve. The solution of the given potential can then be obtained from the solution of this dual potential by a duality transform. The approach is as follows: first to construct the duality family of the given potential, then to find a dual potential which is easier to solve in the family and solve it, and finally to obtain the solution of the given potential by the duality transform. In this paper, as examples, we solve exact solutions for general polynomial potentials.     

黎曼面上的温度对偶性与亏格数g=1和2的弦宇宙学解

考察了一个在引力场g_μv和dilaton场背景下的有限温度玻色弦模型,导出了高亏格黎曼面上能量动量张量满足的对偶关系式;同时,还在四维Robertson–Walker(R–W)度规下证明了弦气体物质作用量的温度对偶不变性,获得了亏格数g=1和2的弦宇宙学解,并研究了运动方程的温度变换性质.     

Pair production and vacuum polarization of vector particles with electric dipole moments and anomalous magnetic moments

The matrix 8-component Dirac-like form of the P-odd equations for boson fields of spin 1 and 0 are obtained and the symmetry group of the equations is derived. We found exact solutions of the field equation for vector particles with arbitrary electric and magnetic moments in external constant and uniform electromagnetic fields. The differential probability of pair production of vector particles with electric dipole moments and anomalous magnetic moments by an external constant and uniform electromagnetic field has been found using exact solutions. We have calculated the imaginary and real parts of the electromagnetic field Lagrangian that takes into account the vacuum polarization of vector particles. Received: 14 April 2001 / Revised version: 13 July 2001 / Published online: 19 September 2001     

Complex Maxwell's equations

A unified complex model of Maxwell’s equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell’s equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac’s quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell’s equations to include longitudinal waves.A formal analogy between this formulation and Dirac’s equation is also discussed.     

Duality Computing in Quantum Computers

In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.     

Duality Computing in Quantum Computers

In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.     

Allowable Generalized Quantum Gates

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.     

Particle nature of light waves in dielectric media

Wave-particle duality is a foundation for modern science. The speed of light waves in dielectric media is less than c. The corresponding particles thus have mass. Combining wave-particle duality with the theory of relativity, an exactly solvable problem was proposed, concerning the transition from photons in vacuum to particles in dielectric media. The rest mass, the momentum, and the total energy of material particles are shown to be the functions of the refractive index of the medium and the wavelength of the incident light. The proposed relationships were applied to study the wavelength-dependent index of refraction of dielectrics and the correlation of the refractive indices of anisotropic crystals, which were confirmed by the experimental results. Variation of the refractive index with wavelength is found to obey the proposed relation. The refractive indices of anisotropic crystals are shown to be the correlated quantities.     

Self-action of intense electromagnetic radiation in an electron-positron vacuum

An analysis is done of the effects of self-action of intense coherent electromagnetic radiation in an electron-positron vacuum that is in homogeneous electric and magnetic fields. A modified version of the Heisenberg-Euler theory, in which the Lagrangian incorporates terms with field derivatives, is used to take into account vacuum dispersion. The nonphysical branch of the solutions of the dispersion equation is excluded by a transition to a quasioptical equation for the slowly varying field envelope, an equation that describes the propagation of radiation with allowance for diffraction, spatial-temporal dispersion, and vacuum nonlinearity. The existence of dark solitons (with an intensity gap) in the vacuum is shown to be present. Finally, self-focusing of radiation in a vacuum is demonstrated and the critical self-focusing power is determined. Zh. éksp. Teor. Fiz. 113, 513–520 (February 1998)     

The Inflationary Solutions with O(2,2) Duality Symmetry in String Cosmologies

The low energy duality string model is investicated in time-dependent metric, torsion, dilaton background fields and potential fields, the inflationary solutions for string cosmologies are obtained when the space-time dimension is D = 3. It is found that the new cosmological solutions can be generated through O(d, d) duality transformations.     

Propagation of gravitational waves in Robertson-Walker backgrounds

The electric and magnetic parts of the linearized Weyl tensor, when the stress-energy tensor is that of a perfect fluid and the background is of Robertson-Walker type, are known to satisfy wave equations that differ by the presence of a source term for the electric part. It is shown here that all of the allowed solutions of the inhomogeneous equation can be obtained by applying a differential operator to the solutions of the homogeneous equation; consequently, electric-type and magnetic-type gravitational waves have the same propagation properties. The results of a complete integration of the appropriately linearized Newman-Penrose equations are given.     

Gravity and duality between coordinates and matter fields

We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection, curvature as well as the Einstein equation are given in this parametrization. We also discuss the local duality between coordinates and quantum fields and the metric in this later reparametrization.     

Quasi-topological electromagnetism:Dark energy,dyonic black holes,stable photon spheres and hidden electromagnetic duality

We introduce the quasi-topological electromagnetism which is defined to be the squared norm of the topological 4-form F ∧ F. A salient property is that its energy-momentum tensor is of the isotropic perfect fluid with the pressure being precisely the opposite to its energy density. It can thus provide a model for dark energy. We study its application in both black hole physics and cosmology.The quasi-topological term has no effect on the purely electric or magnetic Reissner-Nordstr o¨m black holes, the dyonic solution is however completely modified. We find that the dyonic black holes can have four real horizons. For suitable parameters, the black hole can admit as many as three photon spheres, with one being stable. Another intriguing property is that although the quasitopological term breaks the electromagnetic duality, the symmetry emerges in the on-shell action in the Wheeler-De Witt patch. In cosmology, we demonstrate that the quasi-topological term alone is equivalent to a cosmological constant, but the model provides a mechanism for the dark energy to couple with other types of matter. We present a concrete example of the quasi-topological electromagnetism coupled to a scalar field that admits the standard FLRW cosmological solutions.     

Bessel光束的矢量分析及其能流密度的特征

通过比较自由空间Besssel光束标量解E(r,t)满足的方程和光场矢量E(r,t)与矢量势A(r,t)之间的关系表达式,利用Bessel的特点,合理构造了矢量势A(r,t)的具体形式,推导出电场量E(r,t)的磁场量B(r,t)各分量满足的具体形式。通过数值计算,给出电场E(r,t)在不同参数θ,φ下与径向坐标ρ之间的关系图线(图1,图2),发现由方程(6)描述的标量解仅是矢量场E(r,t)(方程15描述)在小θ下的近似。通过对能量传输特性的讨论,说明“超光速”的提法是不恰当的。