[Paper Review] New gauge invariant interactions of 1-form and 2-form gauge potentials

Friedemann Brandt, Norbert Dragon|arXiv (Cornell University)|Sep 2, 1997

Quantum Chromodynamics and Particle Interactions5 citations

TL;DR

This paper constructs a novel four-dimensional gauge theory featuring nonpolynomial, local interactions between 1-form and 2-form gauge potentials, representing a nontrivial deformation of a free gauge theory. The key contribution is a gauge-invariant model with explicit dependence on a deformation parameter (gauge coupling), preserving locality and gauge symmetry while introducing higher-order, non-polynomial interactions.

ABSTRACT

A new four dimensional gauge theory with nonpolynomial but local interactions of 1-form and 2-form gauge potentials is constructed. The model is a nontrivial deformation of a free gauge theory with nonpolynomial dependence on the deformation parameter (= gauge coupling constant).

Motivation & Objective

• To develop a new class of gauge theories involving both 1-form and 2-form gauge potentials with nonpolynomial interactions.
• To ensure the resulting theory remains gauge-invariant and local despite the nonpolynomial structure.
• To generalize free gauge theories by introducing a deformation parameter that controls the strength of interactions.
• To explore the implications of nonpolynomial dependence on the gauge coupling in higher-rank form theories.
• To construct a consistent, interacting gauge theory beyond standard polynomial interactions in higher-form gauge fields.

Proposed method

• The model is constructed as a nontrivial deformation of a free gauge theory with 1-form and 2-form potentials.
• Nonpolynomial interactions are introduced through a deformation parameter that acts as the gauge coupling constant.
• Gauge invariance is maintained by carefully structuring the interaction terms to transform covariantly under both 1-form and 2-form gauge transformations.
• The action is built to be local, ensuring causality and compatibility with standard quantum field theory frameworks.
• The construction relies on a systematic deformation procedure that preserves the algebraic structure of the gauge symmetry.
• The resulting theory is shown to be consistent at the level of the action and gauge symmetry algebra.

Experimental results

Research questions

• RQ1 Can a local, gauge-invariant theory be constructed with nonpolynomial interactions between 1-form and 2-form gauge potentials?
• RQ2 How does the deformation parameter influence the structure of interactions in a higher-rank gauge theory?
• RQ3 What is the role of gauge invariance in maintaining consistency when introducing nonpolynomial terms?
• RQ4 Can such a theory be viewed as a deformation of a free gauge theory while preserving locality and symmetry?
• RQ5 What are the implications of nonpolynomial dependence on the gauge coupling for the dynamics of higher-rank forms?

Key findings

• The constructed theory is a consistent, local, and gauge-invariant deformation of a free gauge theory involving 1-form and 2-form potentials.
• The interaction terms are nonpolynomial in the gauge potentials but remain local and preserve gauge symmetry.
• The deformation parameter, interpreted as the gauge coupling constant, controls the strength of the nonpolynomial interactions.
• The model extends the class of known gauge theories beyond polynomial interactions, offering a new class of interacting higher-rank form theories.
• The theory maintains the algebraic structure of gauge symmetry despite the nonpolynomial dependence on the fields.
• The construction demonstrates that nonpolynomial interactions can be systematically incorporated into gauge theories without breaking gauge invariance or locality.