Related papers: Structured Gaussians From Geometric Quantisation
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
We provide a general decomposition of the two-photon state produced by spontaneous parametric down-conversion in Hermite-Gaussian modes, in the case that the pump beam is described by a Hermite-Gaussian beam of any order. We show that the…
A generalized family of scalar structured Gaussian modes including helical-Ince--Gaussian (HIG) and Hermite--Laguerre--Gaussian (HLG) beams is presented with physical insight upon a hybrid topological evolution nature of multi-singularity…
We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by $D$ spatial coordinates and $D(D-1)/2$ tensorial degrees…
We study the structure of the phase space of generic models of deformed special relativity that gives rise to a definition of velocity consistent with the deformed Lorentz symmetry. As a byproduct we also determine the laws of…
We present an algorithm for holographic shaping of partially coherent light, bridging the gap between traditional coherent and geometric optical approaches. The description of partially coherent light relies on a mode expansion formalism,…
In this article a description of the reduced phase space of the standard model coupled to gravity is given. For space or time-like boundaries this is achieved as the reduction of a symplectic space with respect to a coisotropic submanifold…
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…
We develop a systematic Hamiltonian formulation for a gravitating topological matter system in three-dimensional spacetime, coupling a scalar gauge field and a rank-2 antisymmetric gauge field to Einstein--Cartan gravity. We perform the…
The structure of state vector space for a general (non-anomalous) gauge theory is studied within the Lagrangian version of the $Sp(2)$-symmetric quantization method. The physical {\it S}-matrix unitarity conditions are formulated. The…
We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
Geometric Phase in Quantum Mechanics is generally formulated entirely in terms of geometric structure of the Complex Hilbert Space. We will exploit this fact in case of mixed states for three level open systems undergoing depolarization…
Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…