Studies on Carrollian Quantum Field Theories

TL;DR

This paper explores the quantum field theory of Carrollian models, emphasizing gauge fixing and analyzing scalar, fermionic, and electrodynamic cases, revealing gauge dependencies and trivialities in certain theories.

Contribution

It provides a detailed quantum field description of Carrollian theories, highlighting gauge fixing importance and identifying triviality in some abelian cases.

Findings

Gauge fixing is crucial in Carrollian quantum theories.

Scalar Carrollian electrodynamics exhibits gauge-dependent mass.

Some abelian Carrollian theories are loop correction free and trivial.

Abstract

We examine the quantum field description of massive Carrollian field theories, emphasizing the critical role of gauge fixing within the Carrollian sector. We illustrate this importance using scalar Carrollian Electrodynamics (sCED) as a primary example. We also present the quantum field description for complex Carrollian scalar fields, Carrollian fermions, and Carrollian Electrodynamics. We highlight the challenges in scalar Carrollian electrodynamics (sCED), where the renormalized mass appears gauge-dependent, and clarify this discrepancy by carefully constructing completely gauge-fixed propagators. We discuss how certain abelian Carrollian field theories do not admit any loop corrections and are trivial in that sense.