Basis Tensor Gauge Theory

TL;DR

This paper introduces basis tensor gauge theory, a reformulation of gauge theories using tensor fields that transform linearly under dual representations, ensuring locality and a bounded Hamiltonian.

Contribution

It develops a novel tensor-based formulation of gauge theories, establishing local fields with linear transformation properties and a new local symmetry.

Findings

Successfully reformulates gauge theories with basis tensor fields.

Ensures the resulting field theory is local and has a bounded Hamiltonian.

Provides a new perspective on gauge degrees of freedom.

Abstract

We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.