Ebook: Spin - From Basic Symmetries to Quantum Optimal Control

This monograph is a fundamental reference for scientists and engineers who encounter spin processes in their work. The author, Ilya Kuprov, derives the concept of spin from basic symmetries and gives an overview of theoretical and computational aspects of spin dynamics: from Dirac equation and spin Hamiltonian, through coherent evolution and relaxation theories, to quantum optimal control, and all the way to practical implementation advice for parallel computers.

From the preface:
It is reasonable to assume that reality is causal, uniform, and isotropic. These
assumptions lead to the conservation of energy, linear momentum, and angular
momentum. When Lorentz invariance is also assumed, the resulting symmetry
group (translations, rotations, inversions, and now space-time boosts) yields only
two conserved quantities. One is the invariant mass; the other is a sum of angular
momentum and something else, which appears because boost generators commute
into rotation generators: special relativity has more ways of rotating things than
Newtonian physics. That extra quantity is called spin.
Common interpretations of spin are smoke and mirrors, born of futile attempts to
visualise the Lorentz group in three dimensions. I decided here to let the algebra
speak for itself, but also to ignore mathematicians, chie fl y Cartan, who had gen-
erated much fog around spin physics. Illustrations are drawn from magnetic reso-
nance, where real-life applications had served to keep the formalism elegant and
clear.
This book breaks with the harmful tradition of taking analytical derivations
below matrix level — there are too many papers and books that painstakingly discuss
every eigenvector. The same applies to perturbation theories, total spin represen-
tations, propagators, … In all those cases, numerical methods in matrix notation are
ten lines of text and five lines of MATLAB. In this book, I pointedly avoid mathematical
spaghetti: derivations only proceed to a point at which a computer can take
over.