Gauge Symmetry As Symmetry Of Matrix Coordinates

TL;DR

This paper introduces a novel perspective on gauge theories by applying symmetry transformations directly to space coordinates, linking noncommutative geometry, lattice formulations, and the large-N limit to deepen understanding of gauge dynamics.

Contribution

It presents a new approach where gauge fields emerge as fluctuations around classical solutions, connecting noncommutative spaces with lattice gauge theories and string theory insights.

Findings

Gauge transformations act on space coordinates, not fields.

Noncommutative parameters relate to lattice spacing.

Strong coupling gauge theories naturally formulated on noncommutative spaces.

Abstract

We propose a new point of view to gauge theories based on taking the action of symmetry transformations directly on the coordinates of space. Via this approach the gauge fields are not introduced at the first step, and they can be interpreted as fluctuations around some classical solutions of the model. The new point of view is connected to the lattice formulation of gauge theories, and the parameter of noncommutativity of coordinates appears as the lattice spacing parameter. Through the statements concerning the continuum limit of lattice gauge theories, this suggestion arises that noncommutative spaces are the natural ones to formulate gauge theories at strong coupling. Via this point of view, a close relation between the large-N limit of gauge theories and string theory can be manifested.