Perfect fluids: Field-theoretical description and gauge symmetry issue

TL;DR

This paper demonstrates that combinations of 2- and 3-form fields can fully describe perfect fluids, including rotating cases, and discusses gauge symmetry issues and their implications for cosmological models.

Contribution

It provides a field-theoretical framework for perfect fluids using 2- and 3-form fields, clarifying gauge symmetry limitations and contrasting with scalar field descriptions.

Findings

2- and 3-form fields can describe perfect fluids including rotation

Non-rotating case: 3-form field relates to cosmological constant

Gauge symmetry breaks with rotation, challenging scalar field equivalence

Abstract

We show that combinations of (in general, non-linear) 2- and 3-form fields analogous to the Maxwell (1-form) field, completely describe perfect fluids, including the rotating ones. In the non-rotating case, the 2-form field in sufficient, and a free 3-form field proves to be equivalent to appearance of the cosmological term in Einstein's equations (the square-root non-linearity corresponding to $\Lambda=0$). The gauge degrees of freedom break down when a rotation is included, but even when they exist, there obviously fails to be realized an equivalence of the 2-form field and the massless scalar one recently claimed by Weinberg.