Related papers: Bases for spin systems and qudits from angular mom…
The spin network simulator model represents a bridge between (generalised) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
The Kirillov-Souriau-Kostant construction is applied to derive the classical and quantum mechanics for the massive spinning particle in arbitrary dimension.
The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli's theory of the spinning electron and some of its many applications in mathematics and physics are…
A general three quark bound state satisfying the Pauli principle, and conserving angular momentum and isospin, is used to investigate the spin structure of nucleons at high $x$. It is shown if {$F_{1n}/F_{1p}$$\to$1/4}, then both $A_{1p}$…
Hedin's equations for the electron self-energy and the vertex were originally derived for a many-electron system with Coulomb interaction. In recent years it has been increasingly recognized that spin interactions can play a major role in…
Quantum plasmas is a rapidly expanding field of research, with applications ranging from nanoelectronics, nanoscale devices and ultracold plasmas, to inertial confinement fusion and astrophysics. Here we give a short systematic overview of…
A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J…
We construct a generalised formalism for group field theories, in which the domain of the field is extended to include additional proper time variables, as well as their conjugate mass variables. This formalism allows for different types of…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
Dipolar coupled homonuclear spins present challenging, yet useful systems for quantum information processing. In such systems, eigenbasis of the system Hamiltonian is the appropriate computational basis and coherent control can be achieved…
We explain the connection between the generalized spin quantities we have recently introduced and standard forms. We show how the calculation of various quantities of interest using these new forms is done. Focusing attention on expectation…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
We study the magnetic structure of the ground state of an itinerant Fermi system of spin-\nicefrac{1}{2} particles with magnetic dipole-dipole interactions. We show that, quite generally, the spin state of particles depend on its momentum,…
3d quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty-seven such systems are…
In the past few years there has been a tumultuous activity aimed at introducing novel conceptual schemes for quantum computing. The approach proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling theory of SU(2)…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables - inaccessible conceptually derived variables; several examples of such variables are given. The focus is…