The quantum state-dependent gauge fields of Jacobi

TL;DR

This paper proposes a novel approach to quantum theory using state-dependent gauge transformations linked to Jacobi vector fields in the complex projective Hilbert space, aiming to address localization and divergence issues in quantum field theory.

Contribution

It introduces a new framework involving state-dependent gauge transformations associated with Jacobi vector fields in the quantum state space, differing from traditional Yang-Mills theories.

Findings

New gauge transformations $U(1) imes U(N-1)$ linked to Jacobi vector fields.

Potential to address localization and divergence problems in QFT.

A different approach to quantum theory of the self-interacting electron.

Abstract

It is commonly understood that the Yang-Mills non-Abelian gauge fields is the natural generalization of the well known Abelian gauge group symmetry $U(1)$ in the electrodynamics. Taking into account that the problems of the localization and divergences in QFT are not solved in the framework of the Standard Model (SM), I proposed a different approach to the quantum theory of the single self-interacting electron. In connection with this theory, I would like attract the attention to the state-dependent gauge transformations $U(1) \times U(N-1)$ associated with the Jacobi vector fields of the geodesic variations in the complex projective Hilbert space $CP(N-1)$ of the unlocated quantum states (UQS's).