标题： 多维宇宙学与广义麦克斯韦场：可积情形 显示英文标题

标题： Multidimensional Cosmology with a Generalized Maxwell Field: Integrable Cases

摘要： 我们考虑偶数维时空(D=2n)中的多维宇宙学，其中包含完美流体和一个保持共形不变性的麦克斯韦场的多维推广( F 场，一个 n-形式)。在具有各向同性物理 3 空间的模型中，发现了一些可积情况：真空模型(在一般情况下是可积的)和一些具有广义方程状态的完美流体模型。它们都包含一个 F 场的成分，在四维中作为额外的标量出现。得到了一个两参数的平坦空间模型族和四个单参数族，包括非平坦空间模型(其中参数是从流体方程状态中得到的常数)。所有这些可积模型都允许包含一个无质量标量场或一个具有超刚方程状态的附加流体。概述了物理共形框架中真空模型的基本性质。 显示英文摘要

摘要： We consider multidimensional cosmologies in even-dimensional space-times (D=2n) containg perfect fluid and a multidimensional generalization of the Maxwell field, preserving its conformal invariance (the F field, an n-form). Among models with an isotropic physical 3-space some integrable cases are found: vacuum models (which are integrable in the general case) and some perfect fluid models with barotropic equations of state. All of them contain a component of the F field appearing as an additional scalar in 4 dimensions. A two-parameter family of spatially flat models and four one-parameter families, including non-spatially flat models, have been obtained (where the parameters are constants from the fluid equation of state). All these integrable models admit the inclusion of a massless scalar field or an additional fluid with ultrastiff equation of state. Basic properties of vacuum models in the physical conformal frame are outlined.