Version 1
: Received: 9 February 2024 / Approved: 9 February 2024 / Online: 9 February 2024 (16:07:16 CET)
Version 2
: Received: 23 February 2024 / Approved: 27 February 2024 / Online: 7 March 2024 (09:33:28 CET)
How to cite:
Stephenson, M.J. Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes. Preprints2024, 2024020599. https://doi.org/10.20944/preprints202402.0599.v1
Stephenson, M.J. Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes. Preprints 2024, 2024020599. https://doi.org/10.20944/preprints202402.0599.v1
Stephenson, M.J. Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes. Preprints2024, 2024020599. https://doi.org/10.20944/preprints202402.0599.v1
APA Style
Stephenson, M.J. (2024). Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes. Preprints. https://doi.org/10.20944/preprints202402.0599.v1
Chicago/Turabian Style
Stephenson, M.J. 2024 "Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes" Preprints. https://doi.org/10.20944/preprints202402.0599.v1
Abstract
We explore nonrelativistic quantum electrodynamics in a background magnetic field, maintaining gauge invariance through a vector potential. The Lagrangian incorporates electron self-interactions and electromagnetic field interactions. The path integral formalism elucidates the effective action, focusing on the photon propagator and screening effects. Analyzing density and current components reveals Laurent expansions in the hydrodynamic limit. Equations of motion in real space are derived, including a discussion on Poiseuille-like flow and the Navier-Stokes equation. Nonrelativistic and relativistic hydrodynamics are discussed, with linearized equations presented. The study concludes with insights into the nonrelativistic limit, providing a comprehensive framework for quantum electrodynamics analysis.
Keywords
nonrelativistic quantum electrodynamics; NRQED; background magnetic field; gauge invariance; Lagrangian; electron self-interactions; electromagnetic field interactions; path integral formalism; effective action; photon propagator; screening effects; density components; current components; Laurent expansions; hydrodynamic limit; equations of motion; Poiseuille-like flow; Navier-Stokes equation; relativistic hydrodynamics; linearized equations; nonrelativistic limit; quantum electrodynamical analysis
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
