CLASSICAL AND QUANTUM SYMMETRIC ELECTROMAGNETISM I: BASIC EQUATIONS

Micho Durdevich

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CLASSICAL AND QUANTUM SYMMETRIC ELECTROMAGNETISM I: BASIC EQUATIONS

机译：经典和量子对称电磁学I：基本方程

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We study algebraic and geometric properties of generalized electromagnetic field configurations. Our basic principle is that electric and magnetic fields are mutually symmetric and interchangeable, much in the spirit of the original Dirac considerations. This leads us to naturally modify Maxwell equations, to make such a symmetry explicit. A subtle refinement of the symmetry concept is required, to adopt the apparent geometrical difference between electric field vectors and magnetic field pseudovectors. The symmetry between two fields leads to a gauge theory setting. The corresponding connection field is introduced and analyzed. The geometrical framework naturally invites to consider an extended space of internal degrees of freedom, by complementing the electromagnetic field with a scalar field, which generates the charge and current densities. The gauge-invariant Maxwell equations are discussed in detail. In particular, the energy and momentum conservation laws are derived. The theory will gradually be developed, and it will include the appropriate quantum space-time structures. The present paper deals with classical special-relativistic space-time only. Illustrative examples are presented.

机译：我们研究广义电磁场配置的代数和几何性质。我们的基本原理是，电场和磁场是相互对称且可互换的，这在很大程度上是原始Dirac考虑的精神。这使我们自然地修改了麦克斯韦方程，使这种对称性变得明确。需要对对称性概念进行细化改进，以采用电场矢量和磁场伪矢量之间的明显几何差异。两个场之间的对称性导致规范理论的建立。介绍并分析了相应的连接字段。几何框架自然会考虑通过使用标量场对电磁场进行补充来考虑内部自由度的扩展空间，该标量场会产生电荷和电流密度。规范不变的麦克斯韦方程被详细讨论。特别地，导出了能量和动量守恒定律。该理论将逐步发展，并将包括适当的量子时空结构。本文只涉及经典的相对论时空。给出了说明性示例。

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《Hadronic Journal》 |2015年第4期|383-428|共46页
作者
Micho Durdevich;
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Instituto de Matematicas, UNAM Area de la Investigacion Cientifica Circuito Exterior, Ciudad Universitaria Mexico DF, CP 04510, Mexico;

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CLASSICAL AND QUANTUM SYMMETRIC ELECTROMAGNETISM I: BASIC EQUATIONS

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