Solution to the Bargmann－Wigner equation for a half-integral spin

A rigorous method to solve the Bargmann－Wigner equation for an arbitrary half-integral spin is presented and explicit relativistic wavefunctions for an arbitrary half-integral spin are deduced.     

Spin Zero Quantum Relativistic Particles in Einstein Universe

We find exact eigenvalues and eigenfunctions of relativistic massless scalar particle conformally coupled to a background Einstein universe.     

Projection Operator and Feynman Propagator for a Free MassiVe Particle of Arbitrary Spin

Based on the solution to the Bargmann-Wigner equations, a direct derivation of the projection operator and Feynman propagator for a free massive particle of arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin, the general commutation rules and Feynman propagator with additional non-covariant terms for a free massive particle with any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, and 4 are provided.     

On Spinning Particles

There exist classical systems whose canonical quantization yields relativistic wave equations. As a constructive proof, the classical mechanics of a translating-rotating five-frame is considered. Its quantization yields the Dirac, Weyl, Klein-Gordon, Maxwell-Proca, and higher spin equations, together with a rotational mass spectrum for the states predicted.     

相对论粒子的自旋算符

发展了关于相对论态自旋算符的系统理论.考虑了具有非零静质量的粒子情况.对带自旋的相对论粒子,通常的自旋算符需换为相对论的自旋算符.在Poincar啨群不可约表示的框架里,构造了适用于粒子任意正则态的自旋算符,称为运动自旋.本文的讨论限于量子力学.随后将在量子场论中对此作进一步深入研究.     

On Decay of Correlations for Unbounded Spin Systems with Arbitrary Boundary Conditions

We propose a method based on cluster expansion to study the truncated correlations of unbounded spin systems uniformly in the boundary condition and in a possible external field. By this method we study the spin–spin truncated correlations of various systems, including the case of infinite range simply integrable interactions, and we show how suitable boundary conditions and/or external fields may improve the decay of the correlations.     

Geometric and Algebraic Approach to Classical Dynamics of a Particle with Spin

We investigate the Frenkel equation and alternative approaches aimed to describe classically the dynamics of a particle with a spin degree of freedom. For all those theories unphysical solutions are shown to exist but to be removable via formal use of geometric perturbation theory. With an Clifford algebraic representation of the employed geometric concepts we put forward the modified Frenkel equation as more intuitive as alternative approaches.     

Spinning Particles in Spacetimes with Torsion

A novel analysis of the Mathisson-Papapetrou-Dixon equations is presented employing mathematical tools that do not rely on the torsion free geometries used in previous literature. A system of differential algebraic equations that can be used to describe the motion of spinning particles in an arbitrary geometry is derived. The curvature in these equations can involve non-Riemannian contributions. Subsequently, this particular system of equations can accommodate modification to geodesic motion from both scalar fields and the spin of the particle. PACS: 02.40.Hw, 04.20.Cv, 04.40.Nr     

原子核反核子谱的自旋对称性

简要介绍原子核反核子谱的自旋对称性。通过分析包含标量势和矢量势的核子及反核子Dirac方程的性质,给出核子谱的赝自旋对称性和反核子谱的自旋对称性的起因。对于反核子双重态,除了它们的能量非常接近以外,它们的波函数也几乎严格地满足自旋对称性所要求的关系。     

Energy-Momentum Properties and the Spin of Short-Lived Particles

The space–time translation property of a stable particle is characterized by a time-like Lorentz vector (E, _k ). We show in this contribution that unstable particles are, in addition, characterized by a space-like Lorentz 4-vector of uncertainties, or spreads, ( E, k). This is true for unstable states created in formation-, in production-, and in decay-experiments. The space-like nature of the spread vector causes a nonzero momentum spread to be present in all Lorentz frames so that there is no Lorentz frame in which the unstable particle is entirely at rest. With the space-like spreadvector ( E, k) in addition to the time-like (E, _k ), also the rotation property of an unstable particle is affected, and unstable states have an uncertainty in their spin. This means neighboring spin states are occupied in addition to the original spin. Experiments are discussed that show a principal limitation of the accuracy of spin measurement from finite lifetimes. Wave functions for unstable particles are discussed, and we show in the example of a short-lived spin-0 state that the appearance of a spin neighbor in the amplitude is proportional to the inverse lifetime.     

自旋不是轨道角动量的相对论效应——与许方官和高春媛商榷

对《大学物理》2000年第11期上发表的《氢原子的磁矩－对自旋的讨论之一》一提出了不同的看法，认为该错把相对论的流密度当成了非相对论的流密度，前不能在非相对论近似下过滤到后，在相对论情况下，自旋和轨道耦合在一起，不能互相独立，在非相对论情况下自旋独立于轨道运动而存在；因而，自旋不是轨道角动量的相对论效应。     

Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences Zitterbewegung, represents a gauge non-invariant variable in our model. Hence our particle does not experience the undesirable Zitterbewegung. C) In the non-relativistic limit spin is described by three-vector, as it could be expected.     

Nucleon Spin Content in a Relativistic Quark Potential Model Approach

Based on a relativistic quark model approach with an effective potential U(r) = (ac/2)(1 + γ0)r2, the spin content of the nucleon is investigated. Pseudo-scalar interaction between quarks and Goldstone bosons is employed to calculate the couplings between the Goldstone bosons and the nucleon. Different approaches to deal with the center of mass correction in the relativistic quark potential model approach are discussed.     

Spin symmetric solutions of Dirac equation with PSschl-Teller potential

The approximate analytical solutions of the Dirac equation with the Poeschl-Teller potential is presented for arbitrary spin-orbit quantum number κ within the framework of the spin symmetry concept. The energy eigenvalues and the corresponding two Dirac spinors are obtained approximately in closed forms. The limiting cases of the energy eigenvalues and the two Dirac spinors are briefly discussed.     

The Entropy of Spherically Symmetric Black Holes Due to Arbitrary Spin Fields

Using the membrane model which is based on brick-wall model, we calculated the free energy and entropy of spherically symmetric black holes due to arbitrary spin. The result shows that the entropy of a scalar field and the entropy of a Fermionic field have similar formulas. There is only a coefficient between them.     

General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

A construction of relativistic wave equations on the homogeneous spaces of the Poincaré group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is shown that a direct product of Minkowski space time and two-dimensional complex sphere is the most suitable homogeneous space for the physical applications. The Lagrangian formalism and field equations on the Poincaré and Lorentz groups are considered. A boundary value problem for the relativistically invariant system is defined. General solutions of this problem are expressed via an expansion in hyperspherical functions defined on the complex two-sphere. PACS numbers: 02.30.Gp, 02.60.Lj, 03.65.Pm, 12.20.-m     

从Sn质子滴线核到Sn中子滴线核的自旋对称性和赝自旋对称性

在球形相对论平均场模型下, 采用NLSH相互作用全面研究了从Sn质子滴线核到Sn中子滴线核的自旋对称性和赝自旋对称性. 发现: 1) 随着核子数的增大, 中子和质子的赝自旋波函数劈裂基本上都是减小的, 并且质子的变化趋势更加明显. 中子高能级的自旋波函数劈裂随着核子数的增大也是减小的. 2) 对于特定的同位素, 当n=1时, 赝自旋波函数劈裂随着l的增大而增大. 当n=2时, 中子的自旋波函数劈裂随着l的增大而增大. 当l=2或l=3时, 中子的自旋波函数劈裂随着n的增大而增大. 3) 中子和质子的赝自旋劈裂之间的差别总是比自旋劈裂的差别更大一些.     

Squeezing for Entangled States of Two Entangled Particles with Different Masses

Using the technique of integration within an ordered product of operators we present a convenient approach for introducing the squeezing operator for the entangled states of two entangled particles with different masses. We also introduce one-sided squeezing operators.