洛伦兹光束的传输特性研究

运用光束传输的二阶矩理论,对洛伦兹光束的传输特性进行了研究,给出了束腰、横向发散角和光束传输因子的表达式.横向束腰仅取决于对应方向上的光束参数;而横向发散角和光束传输因子却取决于两横向上的光束参数.给出了光束传输因子随两横向光束参数的变化关系曲线.结果表明,两横向上的光束传输因子随两光束参数的变化规律是不相同的,而整体的光束传输因子随两光束参数的变化是前两者的综合体现;但在傍轴情形下,光束传输因子趋向于常数141,因此,对于相同束腰,其傍轴条件下的发散性为对应高斯光束的141倍.所以,洛伦兹光束适合用于描述某些发散程度较大的激光光源. 关键词： 洛伦兹光束 光束传输 二阶矩     

Derivation of the Lorentz Boost from the Evans Wave Equation

The Lorentz boost is derived from the Evans wave equation of generally covariant unified field theory by constructing the Dirac spinor from the tetrad in the SU(2) representation space of non-Euclidean spacetime. The Dirac equation in its wave formulation is then deduced as a well-defined limit of the Evans wave equation. By factorizing the dAlembertian operator into Dirac matrices, the Dirac equation in its original first differential form is obtained from the Evans wave equation. Finally, the Lorentz boost is deduced from the Dirac equation using geometrical arguments. A self-consistency check of the Evans wave equation is therefore forged by deducing therefrom the Lorentz boost in the appropriate limit. This procedure demonstrates that the Evans wave equation governs the properties of matter and anti-matter in general relativity and unified field theory and leads both to Fermi-Dirac and Bose-Einstein statistics in general relativity.     

Lorentz Transformations from Reflections: Some Applications

We point out, by exhibiting two examples and mentioning a third one, that it is sometimes useful to consider Lorentz transformations as generated from hyperplane or line reflections. One example concerns the construction of boosts linking two given 4-vectors, the other one concerns the Minkowski geometric understanding of V. Moretti's polar decomposition of orthochronous Lorentz matrices.     

On the quantum Lorentz group

The quantum analog of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indices we construct a quantum Minkowski metric. In this framework we show explicitly the correspondence between the SL(2,C) and Lorentz quantum groups. Five matrices of the quantum Lorentz group are constructed in terms of the R matrix of SL(2,C) group. These matrices satisfy Yang–Baxter equations and two of which have adequate properties tied to the quantum Minkowski space structure as the reality conditions of the coordinates and the symmetrization of the metric. It is also shown that the Minkowski metric leads to invariant and central lengths of four-vectors.     

Relativistic Anandan quantum phase in the Lorentz violation background

We study the influence of a classical background based on the violation of the Lorentz symmetry on the relativistic Anandan quantum phase. We show that the choice of the Lorentz symmetry violation background provides an abelian contribution for the relativistic Anandan quantum phase.     

磁单极与磁洛伦兹力

概述了磁单极概念的历史发展,从洛伦兹变换出发,利用电磁场张量和四维力的协变性以及电荷相对论不变,直接证明了运动磁单极受磁洛伦兹力,建议了一个磁洛伦兹力的验证方案,并用磁洛伦兹力公式导出狄拉克电荷量子化条件．证明了磁洛伦兹力公式具有与库仑定律相同的精确度．     

Lorentz manifolds modelled on a Lorentz symmetric space

We give examples of Lorentz manifolds modelled on an indecomposable Lorentz symmetric space which are geodesically complete and not locally homogeneous.     

On the Meaning of Lorentz Covariance

In classical mechanics, Galilean covariance and the principle of relativity are completely equivalent and hold for all possible dynamical processes. In contrast, in relativistic physics the situation is much more complex. It will be shown that Lorentz covariance and the principle of relativity are not completely equivalent. The reason is that the principle of relativity actually only holds for the equilibrium quantities that characterize the equilibrium state of dissipative systems. In the light of this fact it will be argued that Lorentz covariance should not be regarded as a fundamental symmetry of the laws of physics.     

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by “turns,” which are equivalence classes of directed great circle arcs on the unit sphere S ², in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group SU(1, 1)=Sp(2, R)=SL(2, R), the double cover of SO(2, 1). The present work develops a theory of turns for SL(2, C), the double and universal cover of SO(3, 1) and SO(3, C), rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation. PACS numbers: 02.20.-a     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.     

Lorentz violation from the Higgs portal

We study bounds and signatures of models where the Higgs doublet has an inhomogeneous mass or vacuum expectation value, being coupled to a hidden sector that breaks Lorentz invariance. This physics is best described by a low-energy effective Lagrangian in which the Higgs speed-of-light is smaller than c; such effect is naturally small because it is suppressed by four powers of the inhomogeneity scale. The Lorentz violation in the Higgs sector is communicated at tree level to fermions (via Yukawa interactions) and to massive gauge bosons, although the most important effect comes from one-loop diagrams for photons and from two-loop diagrams for fermions. We calculate these effects by deriving the renormalization-group equations for the speed-of-light of the Standard Model particles. An interesting feature is that the strong coupling dynamically makes the speed-of-light equal for all colored particles.     

Test of Lorentz invariance using optical cavities

This paper indroduces the precision test of Lorentz invariance using ultra-stable and low-loss optical cavities. The effective-field theory widely adopted in the analysis of experimental data has been reviewed. The sensitivity of the cavity resonant frequency to the Lorentz-violating tensor field is discussed in detail. In addition, the polarization of the optical field has been added to the model, and our analysis shows that the frequency shift due to Lorentz violation is not sensitive to the polarization of the optical field.      

On localization of vorticity in Lorentz lattice gases

We study the generalized deterministic Lorentz lattice gases, in a fixed as well as in varying environments, in lattices with dimensionsd3. We show that bounded orbits (vortices) in these models are often contained in some lower dimensional subsets (vortex sheets) of these lattices.     

Discrete Space-Time and Lorentz Symmetry

Recent observations of Ultra High Energy Cosmic rays suggest a small violation of Lorentz symmetry. Such a violation is expected in schemes with discrete/quantized space-time. We examine this situation and suggest tests which could be carried out by, for example NASA's forthcoming GLAST Satellite.     

Aharonov-Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.     

On gravity localization under Lorentz violation in warped scenario

Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane scenario with one extra dimension where he found a non-zero mass for the four-dimensional graviton. This leads to the conclusion that five-dimensional models with LIV are not phenomenologically viable. In this work we re-examine the issue of Lorentz Invariance Violation in the context of higher-dimensional theories. We show that a six-dimensional geometry describing a string-like defect with a bulk-dependent cosmological constant can yield a massless 4D graviton, if we allow the cosmological constant variation along the bulk, and thus can provides a phenomenologically viable solution for the gauge hierarchy problem.     

Information under Lorentz Transformation

In the context of quantum information, we investigate extensively some important classes of a general form of a two-qubit system under Lorentz transformation. It is shown Lorentz transformation causes a decay of entanglement and consequently information loses. On the other hand, it generates entangled states between systems prepared initially in a separable states. The partial entangled states are more robust under Lorentz transformation than maximally entangled states. Therefore the rate of information lose is larger for maximum entangled states compared with that for partially entangled states.     

One-Dimensional Lorentz Gas with Rotating Scatterers: Exact Solutions

The simplest solutions (orbits) to the recently introduced Lorentz gas with rotating scatterers are found by considering its one-dimensional one-particle reduction. This model has only one parameter which can be viewed as the amount of energy transfer between the scatterers and the particle during a collision. Exact solutions of the system are found for several values of this parameter. For some of these values, the dynamics is shown to be in many respects similar to the dynamics of the deterministic Lorentz lattice gases.     

An approximate formula for the diffusion coefficient for the periodic Lorentz gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.     

Weighted power counting and Lorentz violating gauge theories. II: Classification

We classify the local, polynomial, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. We study the structure of such theories and prove that renormalization does not generate higher time derivatives. We work out the conditions to renormalize vertices that are usually non-renormalizable, such as the two scalar-two fermion interactions and the four fermion interactions. A number of four-dimensional examples are presented.