相关论文: Algebraic Models: Coordinates, Scales, and Dynamic…

The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…

The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…

Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…

Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…

We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices.…

The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…

This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincar\'e reduction theory is applied to the Schr\"odinger,…

A complete classification of 2D superintegrable systems on two-dimensional conformally flat spaces has been performed over the years and 58 models, divided into 12 equivalence classes, have been obtained. We will re-examine two…

Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…

We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our approach allows…

We present an algebraic procedure for constructing Hamiltonians with several distinct partial dynamical symmetries (PDSs), of relevance to shape-coexistence phenomena. The procedure relies on a spectrum generating algebra encompassing…

Quantum electrodynamics in $1+1$ dimensions (Schwinger model) on an interval admits lattice discretization with a finite-dimensional Hilbert space, and is often used as a testbed for quantum and tensor network simulations. In this work we…

The loop quantization of the conformal Brans-Dicke cosmology is explored in the spatially flat and Bianchi-I setting. The scalar and conformal constraints governing the canonical model are quantized using the loop techniques. The physical…

We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…

Using a hyperbolic complex plane, we study the realization of the underlying hyperbolic symmetry as an internal symmetry that enables the unification of scalar fields of cosmological and particle physics interest. Such an unification is…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…

We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…

We consider dynamical spherically symmetric spacetimes, which are conformal to the static spherically symmetric metrics, and find new solutions of Einstein equations by symmetry considerations. Our study help us classify various conformal…