Quantization of Carrollian fermions

TL;DR

This paper introduces the first quantized model of interacting Carrollian Dirac fermions, explores their symmetries, and analyzes their renormalization and fixed points within a Carrollian Yukawa framework, with implications for ultralocal interactions.

Contribution

It presents the first example of interacting quantized Carrollian fermions, coupling them to a scalar field, and studies their renormalization and fixed point structure.

Findings

Ultralocal interaction between fermions and scalar field identified.

One-loop renormalization of Carrollian Yukawa theory performed.

Comparison of fixed points with relativistic theories conducted.

Abstract

We provide the first example of interacting quantized Carrollian Dirac fermions and investigate their discrete symmetries, including charge conjugation (C), parity (P), and time reversal (T) transformations. As a toy model, we couple these fermions to a Carrollian scalar field using Carrollian Yukawa theory and compute the tree-level diagram, revealing an ultralocal interaction between the Carrollian fermions and the scalar field. This interaction, widely known as a Dirac delta interaction with time-dependent factor, frequently appears in quantum physics. We then address the renormalization of the theory by employing the Wilsonian procedure at one-loop order. Furthermore, we analyze the fixed points and stability properties of Carrollian Yukawa theory, comparing them with their relativistic counterparts. Beyond the specific Yukawa model studied here, we expect that our framework will have broader applications in Carrollian physics, particularly in understanding ultralocal interactions and their role in condensed matter systems, where similar phenomena arise in strongly correlated and non-relativistic regimes.