It is well known that a magnetic monopole-electric charge system carries an angular momentum in its electromagnetic fields. Here we show that in the Dirac string formulation of magnetic charge the monopole-electric charge system also carries a momentum in its electromagnetic fields. This overlooked field momentum arises from the Coulomb electric field of the electric charge and the solenoidal magnetic field of the Dirac string. This implies that the monopole-charge system must either: (i) carry a ``hidden momentum" in the string, indicating that the string is real, or (ii) that the monopole-charge system violates the center-of-energy theorem. The overall conclusion is that the Dirac monopole with a {\it regulated} Dirac string is not a true monopole, and is not even a good effective description for topological monopoles ({\it e.g.} the 't Hooft-Polyakov monopole outside the core).
Motivated by examples obtained from conformal deformations of spectral triples and a spectral triple construction on quantum cones we propose a new twisted reality condition for the Dirac operator.
We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in that background and consider the effect of various parameters, such as the frequency of the rotating frame, the oscillator's frequency, the string density and other quantum numbers.
From a study of an oscillator in a $4D$ NC spacetime, we establish the Hamilton equations of motion. The formers are solved to give the oscillator position and momentum coordinates. These coordinates are used to build a metric similar to that describing a cosmic string. On this basis, Dirac and Klein-Gordon oscillators are investigated. Their spectrum and dynamics are analysed giving rise to novel interesting properties.
In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum pu with its alternative p_u+mwbf_u(x_u)). In particular, the quantum dynamics is considered for the function f_u(x_u) to be taken as cornell potential, exponential-type potentialand singular potential. For cornell potential and exponential-type potential, the corresponding radial equations can be mapped into the confluent hypergeometric equation and hypergeometric equation separately. The corresponding eigenfunctions can be represented as confluent hypergeometric function and hyperge…
Dirac's original solution of the nontrivial Bianchi identity for magnetic monopoles [Dirac 1948], which redefines the fieldstrength along the Dirac string, diagonalizes the gauge and monopole degrees of freedom. We provide a variant of the Dirac string, which we motivate through a formal expansion of the Bianchi identity. We show how to use our variant prescription to study monopole electrodynamics without reference to a dual potential and provide some applications.
In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory. For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut. By working with the closed string effective action, obtained aft…
Non-commutative world-volume interactions on D-brane and Dirac-Born-Infeld action
通过对Seiberg-Witten微分方程在一条特殊路径上积分，我们将普通的规范场用它们的非对易对应物表示，直到三个非对易规范场。然后，我们使用这种变化的变量，写普通的阿贝尔Dirac Born Infeld作用的非交换领域。由此产生的行动，然后比较各种低能量接触项的世界片微扰弦散射振幅从非交换D $p$膜。我们发现场论和弦论的结果完全一致。因此，它表明微扰弦论知道塞伯格-威滕微分方程的解。
Dynamics of BPS States in the Dirac-Born-Infeld Theory
本文研究了具有横向标量场的Dirac Born Infeld作用量对各种BPS态的动力学性质的影响。我们首先描述了D3膜上的1/2和1/4 BPS态的特征性质，在IIB型弦论图像中，它们可以被解释为终止于D3膜上的F/D弦。然后我们研究了BPS态对膜上无质量场低能激发的响应，其中标量场表示膜的形状涨落，U（1）规范场表示D-膜上开弦激发.这导致识别BPS状态之间的相互作用，包括静态电位和动力学相互作用。
In this work, we study the Aharonov-Casher effect in the $(2+1)$-dimensional Dirac oscillator coupled to an external electromagnetic field. We set up our system in two different scenarios: in the Minkowski spacetime and the cosmic string spacetime. In both cases, we solve exactly the Dirac oscillator and we determine the energy spectrum and the eigenfunctions for the bound states. We verify that in the Minkowski spacetime, the Dirac oscillator spectrum depends linearly on the strength of the magnetic field $B$, and on the Aharonov-Casher phase. In addition, we explicitly obtain the corrections…
In this paper we consider the Dirac oscillator in the context of Doubly General Relativity or Gravity's Rainbow. In order to obtain the energy levels of the Dirac oscillator, we solve the Dirac equation in the cosmic string spacetime modified by gravity's rainbow scenarios described by two rainbow functions. We then obtain that, as a consequence of the modification of the cosmic string line element by the two rainbow functions, the energy levels of the Dirac oscillator are appreciable altered. The results are plotted and compared with the standard case, without gravity's rainbow effects.
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.
In this work, we analyze the influence of noninertial and spin effects on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background. To model this background, we consider a uniform magnetic field, the Aharonov-Bohm effect, and a parameter $η$ generated by a cosmic string. Posteriorly, we determine the bound-state solutions of the system: the Dirac spinor and the relativistic energy spectrum. We verified that this spinor is written in terms of the generalized Laguerre polynomials and this spectrum depends on the effective quantum number $N_r$, angular velocity $Ω$ and par…
In this article, we study topological and noninertial effects on the motion of the two-dimensional Dirac oscillator in the presence of a uniform magnetic field and the Aharonov-Bohm potential. We obtain the Dirac equation that describes the model. Expressions for the wave functions and energy spectrum are derived. The energy spectrum of the oscillator as a function of the various physical parameters involved in the problem is rigorously studied. Finally, we present some analogies between our results and others of the condensed matter physics.
The problem of singularities associated with Dirac strings and closed timelike curves in classical solutions of pure gravity is analyzed here. A method to eliminate these is introduced and established first for the Taub-NUT geometry. This is superceded by a smooth solution of first order field equations, which is defined to be a unique extension of the Taub Universe to a degenerate metric phase. As an additional feature, this framework naturally provides a geometric interpretation of the magnetic charge in the context of gravity theory without matter. Finally, exploiting the two phases of the …
The Hamiltonian formulation of General Relativity: myths and reality
在文献中经常延续的一种传统智慧是：（i）将时空3+1分解为空间和时间是正则处理的同义词，并且这种分解对于任何广义相对论（GR）的哈密顿公式都是必不可少的;（ii）正则处理必然打破GR中空间和时间之间的对称性，并且由此产生的约束代数不是四的代数-维的代数同态;（iii）根据一些作者，这个代数允许一个只导出空间的代数同态，或者根据其他人，一个特定的场依赖和非协变的四维代数同态;（iv）狄拉克的分析[Proc。A 246（1958）333]和ADM [Arnowitt，Deser and Misner，in“Gravitation：An Introduction to Current Research”（1962）227]的GR规范结构是等价的。我们提供了一些一般性的理由，为什么这些声明应该受到质疑。在[Kiriushcheva等人，Phys. Lett. A 372（2008）5101]，现在我们彻底重新检查GR的狄拉克哈密顿公式的所有步骤。我们表明，上述点（i-iii）不能归因于GR的狄拉克哈密顿公式。我们还证明，ADM和狄拉克公式是通过相空间变量从度量$g_{μν}$到推移和移位函数以及三度量$g_{km}$的变换而相关的，这是不规范的。这就证明了第（4）点是不正确的。点（i-iii）仅仅是使用变量的非正则变化的结果，而不是约束系统的哈密顿-狄拉克方法或爱因斯坦理论本身的内在属性。
In this work we study the Dirac equation with vector and scalar potentials in the spacetime generated by a cosmic string. Using an approximation for the centrifugal term, a solution for the radial differential equation is obtained. We consider the scattering states under the Hulthén potential and obtain the phase shifts. From the poles of the scattering $S$-matrix the states energies are determined as well.
It is shown how a string living in a higher dimensional space can be approximated as a point particle with squared extrinsic curvature. We consider a generalized Howe-Tucker action for such a "rigid particle" and consider its classical equations of motion and constraints. We find that the algebra of the Dirac brackets between the dynamical variables associated with velocity and acceleration contains the spin tensor. After quantization, the corresponding operators can be represented by the Dirac matrices, projected onto the hypersurface that is orthogonal to the direction of momentum. A conditi…
