规范,相位因子和杨-米尔斯场--规范场理论在中国续记

文章是在杨-米尔斯场50周年学术报告会上的报告的精简部分.它和作者发表的一组评述互相补充,目的是引介非亚贝尔规范场和量子不可积相位因子,解说作为20世纪物理学主旋律之一的相位因子的物理意义.     

杨-米尔斯规范场理论的创立

本文从物理学史的角度回忆杨米尔斯理论的提出过程, 以及现代物理学家对这个理论的评价, 最后谈谈克莱因1938年的工作。因为篇幅的限制, 不能详谈其中的数学公式的推演。     

规范场理论在中国——为祝杨振宁先生80大寿而作

文章记叙了20世纪70年代到80年代初期，规范场理论研究在中国的历史事实及杨振宁对中国物理理论研究的影响贡献，介绍了杨振宁对中国科学研究、教学的些论述和从中国规范场理论研究中可吸取的教训。     

杨振宁教授荣获富兰克林奖章和鲍威尔奖──杨-米尔斯规范场理论简介

美籍华裔物理学家杨振宁教授,由于他在非阿贝尔规范场理论方面的奠基性工作,荣获富兰克林奖章和１９９５年鲍威尔奖。文章简委介绍非阿贝尔规范场理论及其在物理学发展中的重要地位。     

纤维丛、规范场和杨-米尔斯方程之间的类比——学科融合研究的一条途径

现在，规范场是物理学中重要的研究领域，而纤维丛则是数学中的热门课题.从本质上讲，就是杨-米尔斯方程将规范场与纤维丛二者联系起来，成为它们的理论的发端.本文着重从物理概念出发，分别论述规范场在物理学中、纤维丛在微分几何中相关概念的形成、发展，以及其与杨-米尔斯方程之间的关系，以使更多的相关专业读者能在这一重要的领域中产生探索和创新的热情，进行深入的研究，促进它在物理、数学和相互交叉课题中取得进展.特别是通过矢量势的旋度运算给出杨-米尔斯方程的一种新的数学表达形式，阐明了它的空间属性，由此能更好地将这三者联系起来，可以加深对纤维丛的联络在更深层次的了解，由于此类问题是一个新的研究方向，值得有志者去深入探索.     

Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A maximally generalized Yang-Mills model, which contains, besides the vector part V_μ, also an axial-vector part A_μ, a scalar part S, a pseudoscalar part P, and a tensor part T_μν, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A generalized Yang-Mills model, which contains, besides the vector part V_μ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

Non-abelian Gauge Symmetry for Fields in Phase Space: a Realization of the Seiberg-Witten Non-abelian Gauge Theory

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic presentation of the Seiberg-Witten approach is carried out for non-abelian gauge in order to guide the calculation procedures. These results are realized by starting with the Lagrangian density for the free Dirac field in phase space. Then a field strength is derived, where the non-abelian gauge group is the SU(2), corresponding to an isospin (non-abelian) field theory in phase space. An application to nucleon is then discussed.

     

Lagrangian Form of the Self-Dual Equations for SU(N) Gauge Fields on Four-Dimensional Euclidean Space

By compactifying the four-dimensional Euclidean space into S₂×S₂ manifold and introducing two topological relevant Wess-Zumino terms to H_n≡SL(n, c)/SU(n) nonlinear sigma model, we construct a Lagrangian form for SU(n) self-dual Yang-Mills field, from which the self-dual equations follow as the Euler-Lagrange equations.     

自对偶场与规范场相互作用理论的Faddeev－Jackiw量子化

本文采用Ｆａｄｄｅｅｖ－Ｊａｃｋｉｗ量子化方法，讨论了二维时空中一种自对偶场与规范场的相互作用理论．通过与Ｄｉｒａｃ方法的比较，建立了这两种方法的等价性     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.``     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T²)_local algebra and the generalized Kac-Moody algebra \hat g(T²). In this paper, we construct the linearly realized gauge theory of the SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Yang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.