整数自旋协变波函数

对高自旋态的Bargmann-Wigner方程的解进行了改造,给出了一套系统地构造高自旋态(整数自旋)协变波函数的新方法.利用这种方法,分别构造了任意整数自旋粒子的协变波函数.     

自旋为任意整数的传播子

以自旋为任意整数的自由粒子的波函数(Bargmann-Wigner方程的解)为基础，进一步研究了 自旋为任意整数的投影算符和传播子.证明了Behrends和Fronsdal所构造的投影算符是正确 的.导出了自旋为任意整数的场的一般对易规则和费恩曼传播子的一般表达式. 关键词： 整数自旋 投影算符 对易规则 费恩曼传播子     

自旋为整数的Bargmann-Wigner方程的严格解

从自旋为任意整数的Bargmann-Wigner方程出发,导出了自旋为整数的场的易于求解的相对论性波动方程,在坐标表象中求解此方程,严格导出了自旋为整数的场的场函数.     

Berry联络与吴–杨单极势

通过研究一半整数自旋值的中性粒子在球对称磁场中的Born-Oppenheimer方程,发现在自旋空间Berry联络呈非阿贝尔形式.在绝热近似下,Berry联络相当于阿贝尔形式的吴-杨单极场.由于拓扑的非平庸性,利用纤维丛中截面的概念研究了位形空间的动力学,发现中心势场中粒子的角动量和能量均取量子化值,但数值发生移动,这是纯几何起源的现象.     

浅谈电子统计的“可变性”

 长期以来,人们一直认为,诸如电子等同一类粒子组成的所谓全同粒子系统中,粒子间的相互作用的实现与量子统计规则有密切关系。由此,可把全同粒子分为两类:一类是费米子,具有强烈的排斥作用;另一类是玻色子,可以凝聚到能量最低态。实验发现,粒子的统计性与其自旋的大小之间具有深刻的联系。三维空间中,粒子自旋的大小只可能是整数（包括零）或半整数。当粒子的自旋是半整数时,它是费米子,服从费米统计;当粒子的自旋是整数或零时,它是玻色子,服从玻色统计,服从玻色或费米统计的粒子波函数在粒子的交换下是对称（+）或反对称（-）的,即 φ（x₁,x₂）=±φ（x₂,x₁） 电子的自旋为1/2,是半整数的,因此电子是费米子,服从费米统计,对于交换两个电子,波函数是反对称的.     

Berry联络与吴－杨单极势

通过研究一半整数自旋值的中性粒子在球对称磁场中的Ｂｏｒｎ－Ｏｐｐｅｎｈｅｉｍｅｒ方程，发现在自旋空间Ｂｅｒｒｙ联络呈非阿贝尔形式．在绝热近似下，Ｂｅｒｒｙ联络相当于阿贝尔形式的吴－杨单极场．由于拓扑的非平庸性，利用纤维丛中截面的概念研究了位形空间的动力学，发现中心势场中粒子的角动量和能量均取量子化值，但数值发生移动，这是纯几何起源的现象．     

自旋粒子的相对论波函数

从相对论波动方程和Lorentz变换理论出发，讨论了自旋粒子的相对论波函数，并给出了求相对论粒子高自旋态的方法。     

“微观因果律”可以任意破坏吗?

本文讨论了量子场论模型中的微观因果律的问题,得到在自轭的标量粒子、整数自旋粒子情形并在“入”场的对易子满足平移不变性的要求下可以推导出微观因果律的结果.     

伪自旋对称情形下Rosen-Morse类型势场中相对论粒子的束缚态

在伪自旋对称情形下研究了Rosen-Morse类型势场中相对论粒子的束缚态,利用Nikiforov-Uvarov方法求解了伪自旋对称情形下的Klein-Gordon和Dirac方程,得到了相对论粒子被束缚在Rosen-Morse类型势场的精确束缚态解.     

元激发和准粒子

元激发或准粒子用于描述宏观物体处于低激发态时的物理性质.不同物理模型对应着不同准粒子,这些独立的准粒子的集合体,使本来复杂的多体问题变得易于处理.在三维及以上的空间中,按照粒子的自旋属性,自旋为半奇数的符合费米-狄拉克统计,自旋为整数的符合玻色-爱因斯坦统计.1977年,Leinaas和Myrheim在研究二维空间拓扑性质后,提出一种遵循分数统计规律的准粒子——任意子,随着二维物理系统的发展,任意子从纯理论研究成为实际研究对象.     

Relativistic scalar equations for a particle with an arbitrary spin

Relativistic Poincaré-invariant wave equations for zero-mass and heavy particles with an arbitrary spin are constructed on the basis of special infinite-dimensional representation of the Lorentz group. The equations form a compatible system of linear differential equations for an unknown scalar function and contain spin s as a parameter (arbitrary complex number). It is also shown that the equations obtained in this way include the well-known finite-component wave equations as a special case of half-integral or integral spin.State University, Omsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 39–44, June, 1992.     

Bargmann–Wigner方程与高自旋场方程

在坐标表象中由Bargmann-Wigner方程导出了便于求解的高自旋场方程,并给出了相应的拉氏函数.     

Many-times formalism and Coulomb interaction

We extend here the many-times formalism, formerly used mainly for particles moving in given classical fields, to interacting particles. In order to minimize the difficulties associated with an equal-time interaction, we limit ourselves to nonrelativistic quantum mechanics and a two-particle interaction, such as that corresponding to the Coulomb force between charged particles. We obtain a set of differential equations which are really not consistent, but they serve as a guide to a formulation in terms of integral equations that has the same perturbation expansion as the usual theory for the scattering of particles. The integral equation for two-particle amplitudes can be modified to give the correct theory for bound states, but this is not the case for more than two particles. We expect that this theory can be generalized to a formulation of relativistic quantum mechanics of interacting particles.     

Phase transitions for a continuous system of classical particles in a box

A continuous classical system involving an infinite number of distinguishable particles is analyzed along the same lines as its quantum analogue, considered in [1]. A commutativeC*-algebra is set up on the phase space of the system, and a representation-dependent definition of equilibrium involving the static KMS condition is given. For a special class of interactions the set of equilibrium states is realized as a convex Borel set whose extremal states are characterized by solutions to a system of integral equations. By analyzing these integral equations, we prove the absence of phase transitions for high temperature and construct a phase transition for low temperature. The construction also provides an example of a translation-invariant state whose decomposition at infinity yields states that are not translation-invariant. Thus we have an example in the classical situation of continuous symmetry breaking.This article is a part of the author's doctoral thesis, which was submitted to the mathematics department at Duke University     

Wave functions in geometric quantization

A geometrical way is described to associate quantum states in the sense of geometric quantization to wave functions in the quantum mechanical sense for each relativistic elementary particle. Explicit computations are made in a number of cases: Klein-Gordon and Dirac equations, neutrino and antineutrino Weyl equations, and very general cases of massive and massless particles of arbitrary spin. In this later case one is led in a canonical way to Penrose wave equations.     

Lagrangian dynamics of polarized media with internal spin in general relativity

The complete system of field equations for a polarized medium with internal spin in interaction with an arbitrary set of fields is derived from a four-dimensional action integral. The general results are then specialized to the interaction with an Einstein-Maxwell field. The application to ideal spinning fluids is discussed.     

On Lieb's Conjecture for the Wehrl Entropy¶of Bloch Coherent States

Lieb@s conjecture for the Wehrl entropy of Bloch coherent states is proved for spin 1 and spin 3/2. Using a geometric representation we solve the entropy integrals for states of arbitrary spin and evaluate them explicitly in the cases of spin 1, 3/2, and 2. We also give a group theoretic proof for all spin of a related inequality. Received: 2 March 1999 / Accepted: 7 May 1999     

Wavefunctions for Particles with Arbitrary Spin

By solving rigorously the relativistic wave equations derived from Bargmann-Wigner equation for arbitrary spin,the relativistic wavefunctions in momentum representation for particles with arbitrary spin are deduced.