A Superdimensional Dual-covariant Field Theory

TL;DR

This paper develops a novel unified field theory combining quantum fields and general relativity using covariant differential calculus, introducing dual state vectors, hybrid tensors, and a dynamic connection to describe matter and interactions.

Contribution

It introduces a superdimensional dual-covariant framework with hybrid tensors and a dynamic connection, unifying quantum and gravitational theories without predefined manifold geometry.

Findings

Derivation of covariant Euler-Lagrange equations for matter and geometry.

Introduction of hybrid curvature form as a covariant derivative of the dynamic connection.

Marking the breaking of the superposition principle in quantum field theory.

Abstract

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.