Quantum Field Dynamics in a Uniform Magnetic Field: Description using Fields in Oblique Phase Space

TL;DR

This paper introduces a field transformation to oblique phase-space coordinates, simplifying the analysis of quantum field dynamics in uniform magnetic fields by separating Landau level dynamics and enabling effective lower-dimensional theories.

Contribution

The paper presents a novel transformation to oblique phase-space coordinates that facilitates the study of quantum fields in magnetic fields, especially for deriving effective theories on the lowest Landau level.

Findings

Effective separation of Landau level dynamics.

Simplified construction of lower-dimensional theories.

Applicable to both nonrelativistic and relativistic fields.

Abstract

We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying quantum field dynamics in the presence of external uniform magnetic field: here, the field transformation serves to separate the dynamics within the given Landau level from that between different Landau levels. We apply this formalism to both nonrelativistic and relativistic field theories. In the large external magnetic field our formalism provides an efficient method for constructing the relevant lower-dimensional effective field theories with the field degrees defined only on the lowest Landau level.