压缩算符在自由标量场理论中的推广

引入了一种在量子场论中构造压缩算符的办法:考虑两个具有不同质量的同一标量场的自由哈密顿量,通过博戈留波夫变换,导出广义压缩算符,该算符把一个基态映射到另一个。该算符作用的有效性分别在量子场论的狄拉克表象和薛定谔泛函表象中得到了验证。我们相信,在任意实标量场理论中,只要存在两组以线性变换联系起来的生成湮灭算符,压缩算符就被类似的方法找到。     

超导与规范对称性,希格斯机制与希格斯粒子——电磁学与电动力学中的超导Ⅱ

本文是文献[1]和[2]联合的后继文章,在文中我们依据电磁学和电动力学中的麦克斯韦方程组建立了有质量光子导致导体中的超导现象这一事实的规范不变描写,文献[1]的结果是目前理论选取洛伦兹规范的特殊情形.我们发现在这种规范不变的理论中存在一个零质量的标量场,它可以和规范势的纵向分量相互转化.这正是文献[2]所介绍的2013年诺贝尔物理学奖中著名的希格斯机制,即规范粒子吃掉Goldstone玻色子而产生纵向分量,因而获得质量.这个新引进的零质量标量场对应量子场论中激发Goldstone玻色子的标量场,它可以被看成是一个更一般的两分量复标量场的相角分量.而此推广的复标量场的常数模分量可以被看成是另一个动力学场——希格斯场的真空期望值.希格斯场的激发是希格斯粒子,即所谓上帝的粒子;而光子的质量则起源于希格斯场的真空期望值.     

探寻和发现——见证希格斯粒子或极类似物

进一步的工作将证明它到底是标准模型的最后一个粒子还是新物理的踪迹．大约50年前,三篇几乎同时独立发表的文章奠定了以后将被称为希格斯机制的理论基础．在粒子物理的标准模型中,要求存在一个标量场,它激发出一个自旋为零的粒子,此标量场与其他基本粒子相互作用而赋予它们以质量．希格斯玻色子是标准模型所预言然而最后尚未被发现的粒子．     

暗物质理论研究

正粒子物理主要研究自然界基本粒子以及它们之间的相互作用。考虑电弱对称性破缺之前的粒子物理标准模型和引力,我们知道自然界存在四种基本相互作用:强、弱、超荷和引力相互作用。我们用对称性描述基本粒子和它们之间的相互作用,如庞加莱代数的两个Casimir算子描述了粒子的质量和自旋,引力相互作用是用广义坐标变换(或数学上说微分同胚变换)下的不变性来描述,强、弱和超荷相互作用是用规范理论来描述,其相应的规范群     

反物质和暗能量

 上个世纪,人类在探索宇宙奥秘和物质基本结构及其相互作用的道路上取得了辉煌的成就,建立了描述微观世界的粒子物理标准模型和描述宇观世界的大爆炸宇宙学标准模型。粒子宇宙学将微观世界和宇观世界、粒子物理学和天文学结合起来,研究早期宇宙这一极端条件下的物理规律,探讨基本粒子的相互作用的统一。近代宇宙学研究表明,在宇宙演化过程中经历了暴涨(Inflation)阶段。基于粒子物理的标量场理论,暴涨宇宙学不仅为经典大爆炸宇宙模型中的初始条件和疑难给予了答案,而且提供了一个描述宇宙大尺度结构成因的合理理论,并为近年观测所支持。     

超弦与M理论

 1.弦与相互作用统一理论20世纪物理学的两个最伟大成就是量子论与相对论。量子场论描述微观世界的基本粒子及其相互作用。广义相对论作为引力理论描述像星体、星系、黑洞及宇宙一类大尺度、巨质量体系。理解一般物理系统要么利用量子场论,要么求助于广义相对论,不会交叉动用这两个不同的理论体系。但是的确存在一些极端物理情景既涉及巨质量(需要广义相对论)又牵连极小距离尺度(需要量子场论),这类体系的正确理解必须建立在一个广义相对论与量子场论相互协调的框架内,换句话说就是需要量子引力理论。     

评论:“边界振动的微腔中的二能级原子”

<正>在曲照军等的文章中[1]作者声称他们能够解决腔场影响原子问题.在此我们显示出既然他们用于得到相互作用表象的哈密顿的变换不完备所以他们没有解决该问题.我们知道此相互作用的哈密顿量可表示为(h=1)H=ωa■a+ωmb■b+ω0/2σz+g1(a■σ_+σ+a)+g2a■a(b■+b),(1)这里a和a■是单模量子化场的产生与湮灭算符,而b和b■为量子谐振子的产生与湮灭算符,g1是单模辐射场与原子的乡耦合系数,g2是单模辐射场与振动边界的耦合常数.曲照军等人把哈密顿量(1)分解成自由和相互作用两个哈密顿量H=H0+HI.这里     

关于光子相算符的Weyl对应理论

本文用湮灭算符的极分解的思想来研究单模相算符,指出相算符可以作为量子谐振子海森堡方程的解而被引入。我们还审视量子光学的相算符的经典对应,即用算符的Weyl编序公式和Wigner算符的Weyl排序形式我们直接导出光子相算符的经典Weyl对应,发现它确实对应一个经典相。     

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.     

双模耦合谐振子哈密顿量的一般解法

双模耦合谐振子哈密顿量是广义坐标■和广义动量■的一般二次型,通过一个坐标变换可以将其表示为新基底下的标准二次型,经计算得知,新基底之间满足准正则对易关系,从而引入准粒子的产生和湮没算符,这样就消除了耦合项,哈密顿量化简成为双模独立谐振子情形,使问题得到解决.这样的解决方法可以推广到各向异性n模谐振子的耦合体系.     

Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field φ plays in Brans–Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with φ; and almost all of the fundamental components of our universe can be unified into the dynamical equation for φ. As a generalization of Brans–Dicke theory, we propose a new gravity theory with a complex scalar field ϕ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.     

Determination of the Glueball Mass Spectrum with the Spin-Orbit Interaction

Based on the investigation of the asymptotic behaviour of the polarization loop function for scalar charged particles in an external gauge field we determine the interaction Hamiltonian including the nonperturbative corrections of the relativistic character of motion and the large coupling constant. The mass spectrum of the bound state is analytically derived. The mechanism for arising of the constituent mass of the bound-state forming particles is explained. The change of the bound-state mass and of the constituent mass of particles is analyzed by varying the coupling constant. The mass spectrum of the two-gluon glueball is calculated taking into account spin-orbit and spin-spin interactions.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

On Behavior of Weyl's Gauge Field

We consider a system, consisting of a metric tensor g_μv, a scalar field Φ, a Weyl's gauge field A_μ and a scalar matter field Φ, which is invariant under general coordinate transformation and Weyl's gauge transformation. Two kinds of identities and field equations are given and discussed. A special space-time with g_μv = Φ_-2η_μv is considered in a gauge-independent manner. We point out that in a correct treatment where g_μv is not regarded as an independent variable, an auxiliary condition for Weyl's gauge field cannot be obtained. Therefore Weyl's gauge field can be treated as a usual field.     

Determination of the glueball mass with allowance for the relativistic character of interaction

Nonperturbative corrections to an interaction Hamiltonian that are associated with relativistic motion and a large coupling constant are determined on the basis of an investigation of the asymptotic behavior of the polarization loop for charged scalar particles in an external gauge field. The mass spectrum of a bound state is determined analytically. The mechanism responsible for the emergence of the constituent mass of particles that form a bound state is explained. It is shown that the contribution of the vector potential and the contribution of the potential associated with a nonperturbative character of interaction cancel each other and that the slope of the Regge trajectory is determined in terms of the string tension.     

Conformal invariance and the Higgs boson mass in the Weinberg-Salam theory with gravitational mechanism of instability

The assumption that the Higgs scalar field equation is conformally invariant leads to new features of the unified gauge theories including classical gravitation. Both the self-consistent approach and the external curved space-time method are discussed here. The purpose is to compute the upper and lower bounds on the mass of the stable Higgs particle. Also an attempt to obtain a discrete mass spectrum at classical level was made.     

A quantitative approach to low-energy quantum chromodynamics

A general method for solving the low-energy spectrum of an infrared unstable field theory is presented. The method involves a strong coupling expansion of the lattice approximation to the theory. Ultimately the results must be continued to zero-coupling constant in accord with the asymptotic freedom of such theories. The method is applied to the pure gauge field (glueball) part of quantum chromodynamics. The spectrum of lowest-lying states consists of a scalar and tensor which are almost degenerate and an axial vector with mass ≈1.6 times the scalar mass.The same procedure applied to the Abelian gauge theory yields unstable results which may indicate the presence of a phase transition.     

Confinement from a scalar-gluon coupling in gauge theory

A model is introduced with a massive scalar coupling to the Yang-Mills term in four-dimensional gauge theory. It is shown that the resulting potential of colour sources consists of a short distance Coulomb interaction and a confining part dominating at large distances. Far away from the source the scalar vanishes while the potential diverges linearly. Up to an -dependent factor of order 1 the tension parameter in the model is gmf, where m denotes the mass of the scalar and f is a coupling scale entering the scalar-gluon coupling. Received: 18 May 1998 / Published online: 26 August 1998