Related papers: Bases for spin systems and qudits from angular mom…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…
Quantum annealing leverages the properties of interacting quantum spin systems to solve computational problems, typically optimisation problems. Current hardware now has capabilities that can be used to solve condensed matter physics…
The mathematical apparatus of quantum--mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which…
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
We first propose a general method to construct the complete set of on-shell operator bases involving massive particles with any spins. To incorporate the non-abelian little groups of massive particles, the on-shell scattering amplitude…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…
Approximate but reliable solutions of a quantum system with $N$ identical particles can be easily computed with the envelope theory, also known as the auxiliary field method. This technique has been developed for Hamiltonians with arbitrary…
Sums of matrix elements of spin-dependent two-body momentum-independent interactions and sums of their products are calculated analytically in the basis of many-body states with given total spin --- the states built from spin and spatial…
A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
In the traditional formalism of quantum mechanics, a simple direct proof of (a version of) the Spin Geometry Theorem of Penrose is given; and the structure of a model of the `space of the quantum directions', defined in terms of elementary…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
The pseudo-spin symmetry is reviewed. A mapping that produces the separation of the total angular momentum into pseudo-orbital and pseudo-spin degrees of freedom is discussed, together with the analytic transformations that take us from the…
Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein…
The main aim of this work is to present an explicit construction of a 2-design of ${\rm U}(2)$, relying only on a tool that belongs to every physicists toolbox: the theory of angular momentum. Unitary designs are a rich and fundamental…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
Extending our prior investigation, we give a new off-shell construction of theories of spinning particles propagating in Minkowski spaces with arbitrary $N$-extended supersymmetry on the world-line. The basis of the new off-shell…