扩展对象的同形不变量理论的若干问题I：相对论粒子及其d-膜的性质
Aspects of Diffeomorphism Invariant Theory of Extended Objects I: The Relativistic Particle and its d-brane Cousins
摘要：
研究了经典重参不变物质系统的一般结构，主要是相对论粒子及其$d$ -膜推广。这与电磁场中的相对论性粒子作为重参数化不变系统的情况十分相似。讨论了体空间M中扩张对象（$d$ -膜）的一个同态不变拉格朗日作用量的结构。我们的构造使用一阶齐次拉格朗日函数来实现一般协方差，而不是使用标量拉格朗日函数和度量相关的积分测度。该框架包含内在的相对论性点粒子，弦论，和Dirac-Nambu-Goto拉格朗日。在自然的方式中，物质拉格朗日量包含背景相互作用场，例如类似于电磁矢量势的1-形式场和度量张量。这个框架自然地暗示了超越电磁学和引力的新的经典相互作用场。构造一个相互作用场的拉格朗日量，是背景自由的，并符合规范对称性中提出的运动方程的物质概述。保留字：非同形不变系统，重参数不变物质系统，物质拉格朗日量，齐次奇异拉格朗日量，相对论粒子，弦论，扩展对象，d膜，相互作用场，超越电磁和引力的经典力，一般协变理论，规范对称性，背景自由理论。
英文摘要：
General structure of classical reparametrization-invariant matter systems, mainly the relativistic particle and its $d$-brane generalization, are studied. The exposition is in close analogy with the relativistic particle in an electromagnetic field as reparametrization-invariant system. The structure of a diffeomorphism invariant Lagrangian action for an extended object ($d$-brane) embedded in a bulk space M is discussed. Our construction uses first order homogeneous Lagrangians to achieve general covariance in contrast to the constructions that use scalar Lagrangians along with metric dependent integration measure. The framework contains intrinsically the relativistic point particle, string theory, and Dirac-Nambu-Goto Lagrangians. In a natural way, the matter Lagrangian contains background interaction fields, such as a 1-form field, analogous to the electromagnetic vector potential, and a metric tensor. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. Construction of aninteraction field Lagrangian that is background free and consistent with the gauge symmetries presented in the equations of motion for the matter is outlined. Keywords: diffeomorphism invariant systems, reparametrization-invariant matter systems, matter Lagrangian, homogeneous singular Lagrangians, relativistic particle, string theory, extended objects, d-branes, interaction fields, classical forces beyond electromagnetism and gravity, generally covariant theory, gauge symmetries, background free theories.
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