A longitudinal gauge degree of freedom and the Pais Uhlenbeck field

TL;DR

This paper establishes an equivalence between a longitudinal gauge degree of freedom in a vector field and a Pais-Uhlenbeck scalar field, exploring its interactions, quantization, and potential cosmological implications such as dark energy.

Contribution

It introduces a novel equivalence between gauge degrees of freedom and Pais-Uhlenbeck fields, enabling new insights into their interactions and cosmological roles.

Findings

The gauge degree of freedom is equivalent to a Pais-Uhlenbeck scalar field.

The scalar field interacts with scalars and fermions without altering its dynamics.

The field may be excited by gravitational effects and contribute to dark energy.

Abstract

We show that a longitudinal gauge degree of freedom for a vector field is equivalent to a Pais-Uhlenbeck scalar field. With the help of this equivalence, we can determine natural interactions of this field with scalars and fermions. Since the theory has a global U(1) symmetry, we have the usual conserved current of the charged fields, thanks to which the dynamics of the scalar field is not modified by the interactions. We use this fact to consistently quantize the theory even in the presence of interactions. We argue that such a degree of freedom can only be excited by gravitational effects like the inflationary era of the early universe and may play the role of dark energy in the form of an effective cosmological constant whose value is linked to the inflation scale.