The nonrelativistic limit of the Majorana equation and its simulation in trapped ions

TL;DR

This paper explores the nonrelativistic limit of the Majorana equation, revealing unique features absent in the Dirac equation, and proposes a trapped ion simulation to study these phenomena.

Contribution

It provides a detailed analysis of the Majorana equation at rest and ultrarelativistic limits, and introduces a trapped ion setup for experimental simulation.

Findings

Positive energy solutions can become negative over time.

Nonstandard oscillations occur between real and imaginary components.

Majorana and Dirac equations converge in the ultrarelativistic limit.

Abstract

We analyze the Majorana equation in the limit where the particle is at rest. We show that several counterintuitive features, absent in the rest limit of the Dirac equation, do appear. Among them, Dirac-like positive energy solutions that turn into negative energy ones by free evolution, or nonstandard oscillations and interference between real and imaginary spinor components for complex solutions. We also study the ultrarelativistic limit, showing that the Majorana and Dirac equations mutually converge. Furthermore, we propose a physical implementation in trapped ions.