# Translational anomaly of chiral fermions in two dimensions

## TL;DR

This paper reveals a new quantum anomaly in two-dimensional Weyl fermions, showing that momentum conservation can fail in flat spacetime when coupled to a time-varying electric field, indicating a violation of space-translation symmetry.

## Contribution

It identifies a novel quantum anomaly in flat spacetime, extending the understanding of anomalies beyond gravitational coupling.

## Key findings

- Quantum momentum conservation can fail in flat spacetime.
- Coupling to a time-varying electric field causes space-translation anomaly.
- Highlights a previously unnoted anomaly in quantum field theory.

## Abstract

It is well known that a quantized two-dimensional Weyl fermion coupled to gravity spoils general covariance and breaks the covariant conservation of the energy-momentum tensor. In this brief article, we point out that the quantum conservation of the momentum can also fail in flat spacetime, provided the Weyl fermion is coupled to a time-varying homogeneous electric field. This signals a quantum anomaly of the space-translation symmetry, which has not been highlighted in the literature so far.