Invariants in Polarimetric Interferometry: a non-Abelian Gauge Theory

TL;DR

This paper introduces a gauge theory framework for polarimetric interferometry, creating gauge-invariant quantities called closure traces that improve robustness and provide comprehensive, bias-resistant information for VLBI measurements near black holes.

Contribution

It develops a non-Abelian gauge theory approach to polarimetric interferometry, generalizing closure traces and invariants to enhance measurement robustness and interpretability.

Findings

Closure traces are gauge-invariant and bias-resistant.

The formalism applies to any number of interferometer elements.

The approach identifies a complete set of invariants for interferometric data.

Abstract

The discovery of magnetic fields close to the M87 black hole using Very Long Baseline Interferometry (VLBI) by the Event Horizon Telescope collaboration utilized the novel concept of "closure traces", that are immune to element-based aberrations. We take a fundamentally new approach to this promising tool of polarimetric VLBI, using ideas from the geometric phase and gauge theories. The multiplicative distortion of polarized signals at the individual elements are represented as gauge transformations by general $2\times 2$ complex matrices, so the closure traces now appear as gauge-invariant quantities. We apply this formalism to polarimetric interferometry and generalize it to any number of interferometer elements. Our approach goes beyond existing studies in the following respects: (1) we use triangular combinations of correlations as basic building blocks of invariants, (2) we use well-known symmetry properties of the Lorentz group to transparently identify a complete and independent set of invariants, and (3) we do not need auto-correlations, which are susceptible to large systematic biases, and therefore unreliable. This set contains all the information, immune to corruption, available in the interferometer measurements, thus providing important robust constraints for interferometric studies.