Invariants in Polarimetric Interferometry: a non-Abelian Gauge Theory

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.

8 pages (including references), 1 figure, and 5 appendices. Accepted (in press) in Physical Review Letters. Contains appendices and some text not included in the journal version that give more connections to gauge theory and geometric/Pancharatnam phase. See also companion paper arXiv:2108.11399

References in corpus (2)

• First M87 Event Horizon Telescope Results. VII. Polarization of the Ring
• Invariants in Co-polar Interferometry: an Abelian Gauge Theory

Cited by in corpus (8)

• Invariants in Co-polar Interferometry: an Abelian Gauge Theory
• Search for the Epoch of Reionisation with HERA: Upper Limits on the Closure Phase Delay Power Spectrum
• Prospects of using closure traces directly for imaging in Very Long Baseline Interferometry
• Interferometric Image Reconstruction using Closure Invariants and Machine Learning
• Two-dimensional Light Beam Shape Characterization using Interferometric Closure Amplitudes
• Very-Long Baseline Interferometry Imaging with Closure Invariants using Conditional Image Diffusion
• An Introduction to Single-Antenna Radio Astronomical Polarimetry
• Establishing a relationship between the cosmological 21 cm power spectrum and interferometric closure phases