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.v2
Stephenson, M.J. Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes. Preprints 2024, 2024020599. https://doi.org/10.20944/preprints202402.0599.v2
Stephenson, M.J. Quantum Hydrodynamics in External Magnetic Fields: From Nonrelativistic to Relativistic Regimes. Preprints2024, 2024020599. https://doi.org/10.20944/preprints202402.0599.v2
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.v2
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.v2
Abstract
We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.
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.
