Related papers: The spin contribution to the form factor of quantu…
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
The electromagnetic form factors of spin-1/2 particles are known, but due to historical reasons only half of them are found in many textbooks. Given the importance of the general result, its model independence, its connection to discrete…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
We resolve a number of questions related to an analytic description of electromagnetic form factors of non-Dirac particles with the rest spin 1/2. We find the general structure of a matrix antisymmetric tensor operator. We obtain two…
We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin…
We consider the semiclassical limit of the spectral form factor $K(\tau)$ of fully chaotic dynamics. Starting from the Gutzwiller type double sum over classical periodic orbits we set out to recover the universal behavior predicted by…
We analyze the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued fields, which is given by rectangular W-algebras with su$(M)$ symmetry. The matrix valued extension is expected to be useful for the relation between…
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
We give a direct link between description of Dirac particles in the abstract framework of unitary representation of the Poincar\'e group and description with the help of the Dirac equation. In this context we discuss in detail the spin…
We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states…
For spin-1/2 particles, using a suitable Mach-Zehnder-type setup with a spin-flipper, we argue that it is a direct consequence of the quantum mechanical treatment that an experimentally verifiable \textit{subensemble} mean of the measured…
We derive the radial action of a spinning probe particle in Kerr spacetime from the worldline formalism in the first-order form, focusing on linear in spin effects. We then develop a novel covariant Dirac bracket formalism to compute the…
The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the…
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that an operator corresponds to the rate of the proper time and that the operator contains terms which…
We address the propagation of the spin along classical trajectories for a 1/2-spin particle obeying the Dirac equation with scalar potentials. Focusing on classical trajectories as the exact propagation of wave-function discontinuities we…
We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor $K(t)$ analytically for a minimal Floquet circuit model that has a $U(1)$ symmetry…
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…