ROBIN DAMION Robin.Damion@nottingham.ac.uk
Research Fellow
Grassmann variables and pseudoclassical Nuclear Magnetic Resonance
Damion, Robin A
Authors
Contributors
ROBIN DAMION Robin.Damion@nottingham.ac.uk
Researcher
Abstract
The concept of a propagator is useful and is a well-known object in diffusion NMR experiments. Here, we investigate the related concept; the propagator for the magnetization or the Green's function of the Torrey-Bloch equations. The magnetization propagator is constructed by defining functions such as the Hamiltonian and Lagrangian and using these to define a path integral. It is shown that the equations of motion derived from the La-grangian produce complex-valued trajectories (classical paths) and it is conjectured that the end-points of these trajectories are real-valued. The complex nature of the trajectories also suggests that the spin degrees of freedom are also encoded into the trajectories and this idea is explored by explicitly modeling the spin or precessing magnetization by anticommuting Grassmann variables. A pseudoclassical Lagrangian is constructed by combining the dif-fusive (bosonic) Lagrangian with the Grassmann (fermionic) Lagrangian, and performing the path integral over the Grassmann variables recovers the original Lagrangian that was used in the construction of the propagator for the magnetization. The trajectories of the pseudoclassical model also provide some insight into the nature of the end-points.
Citation
Damion, R. A. (2016). Grassmann variables and pseudoclassical Nuclear Magnetic Resonance. Diffusion Fundamentals, 26, 1-23
Journal Article Type | Article |
---|---|
Publication Date | 2016-12 |
Deposit Date | Dec 14, 2022 |
Publicly Available Date | Dec 14, 2022 |
Electronic ISSN | 1862-4138 |
Peer Reviewed | Peer Reviewed |
Volume | 26 |
Article Number | 1 |
Pages | 1-23 |
Keywords | NMR; Nuclear magnetization; propagator; Grassmann numbers; pseudoclassical mechanics; diffusion; path integral |
Public URL | https://nottingham-repository.worktribe.com/output/14888556 |
Publisher URL | https://diffusion.uni-leipzig.de/contents_vol26.php |
Files
Damion2016
(790 Kb)
PDF
You might also like
Deuterium brain imaging at 7T during D2O dosing
(2022)
Journal Article
Observation of angular dependence of T1 in the human white matter at 3T
(2019)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: discovery-access-systems@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search