扩展对象的同形不变量理论的若干问题
Aspects of Diffeomorphism Invariant Theory of Extended Objects
摘要：
通过将电磁场中的相对论性粒子类比为一个重参数化不变的系统，讨论了嵌入体空间M中的扩展对象W的重态不变拉格朗日量的结构.目前的结构自然包含相对论性点粒子、弦论和狄拉克-南武-后藤拉格朗日与韦斯-祖米诺条款。对于Lorentz度规场，只要膜不改变背景相互作用场，则整体浸没W膜的非相对论性理论是很好的定义。一个自然的时间规范是固定的积分淹没（子流形结构）内的洛伦兹签名结构。一般协变相对论理论的讨论膜拉格朗日也进行了讨论。质量壳约束和Klein-Gordon方程被证明是普遍的类引力相互作用时，本。给出了W膜的Dirac方程的一种构造方法，它通过将速度坐标提升为非对易的Gamma变量，从而避免了与这种拉格朗日函数的同形不变性相关的一些问题。
英文摘要：
The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is reparametrization-invariant. The current construction naturally contains, relativistic point particle, string theory, and Dirac--Nambu--Goto Lagrangians with Wess--Zumino terms. For Lorentzian metric field, the non-relativistic theory of an integrally submerged W-brane is well defined provided that the brane does not alter the background interaction fields. A natural time gauge is fixed by the integral submergence (sub-manifold structure) within a Lorentzian signature structure. A generally covariant relativistic theory for the discussed brane Lagrangians is also discussed. The mass-shell constraint and the Klein--Gordon equation are shown to be universal when gravity-like interaction is present. A construction of the Dirac equation for the W-brane that circumvents some of the problems associated with diffeomorphism invariance of such Lagrangians by promoting the velocity coordinates into a non-commuting gamma variables is presented.
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