Hidden Gauge Symmetry in Holomorphic Models

TL;DR

This paper reveals a hidden gauge symmetry in complex holomorphic systems, linked to the Cauchy-Riemann equations, enabling different projections from complex to real phase space and impacting the understanding of their physical properties.

Contribution

It demonstrates that all holomorphic systems inherently possess a hidden gauge symmetry connected to the Cauchy-Riemann equations, and explores the implications for phase space projections.

Findings

Holomorphic systems have an intrinsic gauge symmetry.

Gauge fixing allows multiple projections from complex to real phase space.

Different projections are gauge related in complex space but not in real space.

Abstract

We study the effect of a hidden gauge symmetry on complex holomorphic systems. For this purpose, we show that intrinsically any holomorphic system has this gauge symmetry. We establish that this symmetry is related to the Cauchy-Riemann equations, in the sense that the associated constraint is a first class constraint only in the case that the potential be holomorphic. As a consequence of this gauge symmetry on the complex space, we can fix the gauge condition in several ways and project from the complex phase-space to real phase space. Different projections are gauge related on the complex phase-space but are not directly related on the real physical phase-space.