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Related papers: Geometric quantization via cotangent models

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We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…

dg-ga · Mathematics 2008-02-03 A. V. Aminova , D. A. Kalinin

I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…

General Physics · Physics 2015-06-19 Andrei T. Patrascu

We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes…

Mathematical Physics · Physics 2009-11-10 Leonardo Patino , Hernando Quevedo

Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…

Quantum Physics · Physics 2019-10-11 Guillaume Aubrun , Ludovico Lami , Carlos Palazuelos

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…

High Energy Physics - Theory · Physics 2018-06-13 Mattias N. R. Wohlfarth

Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…

General Relativity and Quantum Cosmology · Physics 2014-12-05 Craig J. Hogan

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We…

General Relativity and Quantum Cosmology · Physics 2015-05-20 J. Fernando Barbero G. , Eduardo J. S. Villaseñor

Let $M$ be a compact K\"ahler manifold equipped with a pre-quantum line bundle $L$. In [9], using $T$-symmetry, we constructed a polarization $\mathcal{P}_{\mathrm{mix}}$ on $M$, which generalizes real polarizations on toric manifolds. In…

Symplectic Geometry · Mathematics 2023-01-04 Naichung Conan Leung , Dan Wang

Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show…

Quantum Physics · Physics 2015-06-10 Marco Cianciaruso , Thomas R. Bromley , Wojciech Roga , Rosario Lo Franco , Gerardo Adesso

Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology, and life sciences. For arbitrary multiparticle…

Quantum Physics · Physics 2016-10-24 Marco Cianciaruso , Thomas R. Bromley , Gerardo Adesso

The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…

Quantum Physics · Physics 2007-05-23 B. A. Nikolov , D. A. Trifonov

I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…

General Relativity and Quantum Cosmology · Physics 2015-02-18 Andrei T. Patrascu

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…

High Energy Physics - Theory · Physics 2018-05-31 Gabriel Herczeg , Andrew Waldron

By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric…

Quantum Algebra · Mathematics 2007-05-23 Martin Schlichenmaier

Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized…

Quantum Physics · Physics 2009-11-10 Rolando Somma , Gerardo Ortiz , Howard Barnum , Emanuel Knill , Lorenza Viola

We derive the quantization map in geometric quantization of symplectic manifolds via the Poisson sigma model. This gives a polarization-free (path integral) definition of quantization which pieces together most known quantization schemes.…

Symplectic Geometry · Mathematics 2024-05-14 Joshua Lackman

We provide a complete quantization for the Gowdy model with local rotational symmetry in vacuum. We start with a redefinition of the classical constraint algebra such that the Hamiltonian constraint has a vanishing Poisson bracket with…

General Relativity and Quantum Cosmology · Physics 2017-06-21 Javier Olmedo , Daniel Martín de Blas , Tomasz Pawłowski

We describe a class of exactly soluble models for gravitational collapse in spherical symmetry obtained by patching dynamical spherically symmetric exterior spacetimes with cosmological interior spacetimes. These are generalizations of the…

General Relativity and Quantum Cosmology · Physics 2013-05-29 Benjamin K. Tippett , Viqar Husain

We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Miguel Campiglia , Cayetano Di Bartolo , Rodolfo Gambini , Jorge Pullin

We propose a geometry-specific, mode-selective quantization scheme in coupled field-emitter systems which makes it easy to include material and geometrical properties, intrinsic losses as well as the positions of an arbitrary number of…