超维对偶协变场论
A Superdimensional Dual-covariant Field Theory
摘要：
在协变微分学的基础上，提出了统一场论（UFT）的方法，试图建立量子场论（QFT）和广义相对论（GTR）的统一。引入由N维统一流形（UM）变量的协变和逆变N分量函数组成的对偶态矢量场（DSV）来表示物质。DSV应该以不同于UM变量的微分的方式进行变换。因此，混合张量和混合仿射张量（动态连接，DC）的介绍。混合曲率形式（HCF）被引入作为DC的协变导数。导出了DSV、DC和一对三元混合张量（分裂度量，SM）的协变欧拉-拉格朗日（EL）方程组。基于一系列适用于UFT的原则，包括UM空间的齐次性、微分不可约性和尺度不变性，构造了标量拉格朗日形式。流形几何的类型不是预先指定的，在局部（签名）或区域（拓扑）方面都不是。DSV方程在UM空间中扮演Schroedinger-Dirac方程的角色。通过相应的EL方程，DC和SM被连接到DSV，并成为负责系统的非线性特征，即相互作用。在本文中，我们标志着打破了现代QFT的背景范式，叠加原理。UM-MF维度的问题将得到解决，QFT和GTR的原则和方法的关系将被讨论。
英文摘要：
An approach to a Unified Field Theory (UFT) is developed as an attempt to establish unification of the Theory of Quantum Fields (QFT) and General Theory of Relativity (GTR) on the background of a covariant differential calculus. A dual State Vector field (DSV)consisting of covariant and contravariant N-component functions of variables of a N-dimensional unified manifod (UM)is introduced to represents matter. DSV is supposed to transform in a way distinct from that of the differentials of the UM variables. Consequently, the hybrid tensors and a hybrid affine tensor (Dynamic Connection, DC) are introduced. The hybrid curvature form (HCF) is introduced as a covariant derivative of DC. A system of covariant Euler-Lagrange (EL) equations for DSV, DC, and a twin couple of the triadic hybrid tensors (Split Metric, SM)is derived. A scalar Lagrangian form is composed based on a set of principles suited for UFT, including the homogeneity in the UM space, differential irreducibility and scale invariance. The type of the manifold geometry is not specified in advance, in neither local (signature) nor regional (topology) aspects. Equations for DSV play role of the Schroedinger-Dirac equation in space of UM. By the correspondent EL equations, DC and SM are connected to DSV and become responsible for the non-linear features of the system i.e. interactions. In this paper we mark breaking of a background paradigm of the modern QFT, the superposition principle. The issue of the UM-MF dimensionality will be addressed, and relations to the principles and methodology of QFT and GTR will be discussed.
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