Gauge gravitation theory

The particularity of the gauge gravitation theory is that Dirac fermion fields possess only Lorentz exact symmetries. It follows that different tetrad gravitational fieldsh define nonisomorphic representations _h of cotangent vectors to a space-time manifoldX ⁴ by Dirac's-matrices on fermion fields. One needs these representations in order to construct the Dirac operator defined in terms of jet spaces. As a consequence, gravitational fieldsh fail to form an affine space modeled after any vector space of deviationsh'–h of some background fieldh. They therefore fail to be quantized in accordance with the familiar quantum field theory. At the same time, deformations of representation _h describe deviations ofh such thath + is not a gravitational field. These deviations form a vector space, i.e., satisfy the superposition principle. Their Lagrangian, however, differs from familiar Lagrangians of gravitation theory. For instance, it contains masslike terms.     

规范场和爱因斯坦

文章讨论的主题是现代非亚贝尔规范场的理论思想．文章说明了这个理论思想是承传、推广和拓展了爱因斯坦的物理思想、目标和原则．规范场理论把爱因斯坦后半生努力奋斗而未能达到的目标提到现实，更加迫近和部分地圆了爱因斯坦的梦想。     

Gauge theory of gravity

General relativity is formulated in the framework of Yang-Mills theory whose gauge group isO(3, 2). This theory allows the global topological charge of spin without breaking Bianchi identity. β function in the renormalization group equation is negative and the confinement of gravity is expected. The confinement radius is, however, actually infinite and we can read off the relation that the average mass density of the present universe is exactly equal to the critical value ρ _c (t)=6H ²(t)/K ².     

Gauge theory of dislocations

In this continuation of work by the author the notion of the distortion of an ideal crystal structure is generalized and the gauge field is defined, fundamental states (vacuum configurations) of which are the crystal structure elementary distortions due to dislocations. The form of the structure equations of the connection form defined by this gauge field is discussed.     

规范场理论和金融市场模型

文章介绍近年理论物理在金融学市场建模中的应用的一个新方向，与一般的数学建模不同，它是应用几何结构的模型，建立在规范场的物理思想和纤维丛的几何结构的基础上，文章介绍了规范场的物理概念思想原则，也介绍纤维丛数学概念和几何结构，然后说明规范场理论与纤维丛理论的相结合，成为与金融市场概念和运作相匹配的市场模型，举出这一模型成功引导出金融市场产品定价的Black—Scholes方程和公式。文章对象以物理学者为主，对于理论经济学、金融理论和系统科学的读者来说可略去数学推导。     

规范场理论和金融市场模型

文章介绍近年理论物理在金融学市场建模中的应用的一个新方向,与一般的数学建模不同,它是应用几何结构的模型,建立在规范场的物理思想和纤维丛的几何结构的基础上.文章介绍了规范场的物理概念思想原则,也介绍纤维丛数学概念和几何结构,然后说明规范场理论与纤维丛理论的相结合,成为与金融市场概念和运作相匹配的市场模型,举出这一模型成功引导出金融市场产品定价的Black-Scholes方程和公式.文章对象以物理学者为主,对于理论经济学、金融理论和系统科学的读者来说可略去数学推导.     

Gauge theory on noncommutative spaces

We introduce a formulation of gauge theory on noncommutative spaces based on the notion of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases. Received: 6 March 2000 / Published online: 8 May 2000     

Gauge technique and BCS theory of superconductivity

Summary The gauge technique in unbroken (exact) relativistic quantum electrodynamics is applied to the nonrelativistic BCS theory exhibiting spontaneously brokenU(1) gauge invariance. In addition to the BCS-type solution, we find an interestingnew solution forweak coupling exhibiting ahigh T _c. The authors of this paper have agreed to not receive the proofs for correction.     

Gauge identities in dual field theory

In the dual and fermion proposed by Neveu, Schwarz and Ramond, we find gauge identities involving vertex parts and also off-shell supergauge identities. When their models are translated into the secondary quantized field theory, we no longer can impose the gauge identities as operator ones, since they would lead to a contradiction of the second-quantization rules. We therefore require weak forms of the gauge identities just in an analogous way to the Lorentz condition in quantum electrodynamics. It is then shown that the weak forms of the identities are consistent with the second-quantization rules and also with field equations.     

Gauge theory on a random lattice

A general formulation of gauge theory on a random lattice is developed and the strong coupling limit of the Wilson string tension worked out. The confining force found in this strong coupling limit is identical to that predicted by the relativistic string model. In particular, the force between two color-triplet charges is a constant for large separation and the tube of electric flux joining the charges fluctuates, giving it a net thickness proportional to the logarithm of its length.     

Gauge theory of the star product

The choice of a star product realization for non-commutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. The covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for non-commutative theories.     

Gauge fields and interactions in matrix string theory

It is shown that all possible N sheeted coverings of the cylinder are contained in type IIA matrix string theory as non-trivial gauge field configurations. Using these gauge field configurations as backgrounds the large N limit is shown to lead to the type IIA conformal field theory defined on the corresponding Riemann surfaces. The sum over string diagrams is identified as the sum over non-trivial gauge backgrounds of the SYM theory.