电-弱相互作用的拉格朗日量在八元数代数中的推广

On the hamiltonian formulation of an octonionic integrable extension for the Korteweg-de Vries equation

We present in this work the hamiltonian formulation of an octonionic extension for the Korteweg-de Vries equation. The formulation takes into account the non commmutativity and non associativity of the implicit algebra which defines the equation. We also analize the Poisson structure of the hamiltonian formulation. We propose a parametric master Lagrangian which contains the two hamiltonian structures of the integrable octonionic equation.

八元离子电动力学

Octonionic Electrodynamics

在分裂八元数代数中导出了真空中的狄拉克算符和麦克斯韦方程。给出了从满八元数方程到经典Maxwell-Heaviside方程的近似。经典电动力学中磁单极子的不存在与结合论极限的应用有关。

分裂八元数中的 Dirac 与 Maxwell 系统

Dirac and Maxwell systems in split octonions

本文利用分裂八元数表示 SO(4,4)/Spin(4,4) 及三线性不变量，构造推广 Dirac 与 Maxwell 系统的 Lagrangian，并证明其方程对应分裂八元数解析性条件。

收缩规范群修正电弱模型的极限情形

Limiting Case of Modified Electroweak Model for Contracted Gauge Group

提出了在物质场空间中对三维球几何电弱模型的修正。该模型的拉格朗日量由{ \it free}（不含任何势项）物质场拉格朗日量和标准规范场拉格朗日量之和给出。矢量玻色子质量通过将该拉格朗日量从笛卡尔坐标变换到球$S_3$上的坐标而产生。讨论了修正模型玻色子部分的极限情况，它对应于收缩规范群$SU(2;j)\times U(1)$。在极限模型的框架内，Z玻色子和电磁场可以看作是W玻色子场的外场，因为W玻色子场不影响这些外场。电弱模型中所有粒子的质量保持不变，但与标准电弱模型相比，收缩模型中的场相互作用更为简单。

Lagrangian formulation, generalizations and quantization of null Maxwell's knots

Knotted solutions to electromagnetism are investigated as an independent subsector of the theory. We write down a Lagrangian and a Hamiltonian formulation of Bateman's construction for the knotted electromagnetic solutions. We introduce a general definition of the null condition and generalize the construction of Maxwell's theory to massless free complex scalar, its dual two form field, and to a massless DBI scalar. We set up the framework for quantizing the theory both in a path integral approach, as well as the canonical Dirac method for a constrained system. We make several observations abo…