scholarly journals Kitaev’s Quantum Double Model from a Local Quantum Physics Point of View

2015 ◽  
pp. 365-395 ◽  
Author(s):  
Pieter Naaijkens
Keyword(s):  
Quantum Physics ◽  
Point Of View ◽  
Quantum Double ◽  
Local Quantum

Double-bosonization of braided groups and the construction of Uq(g)

1999 ◽  
Vol 125 (1) ◽  
pp. 151-192 ◽  
Author(s):  
S. MAJID
Keyword(s):  
Hopf Algebra ◽  
Quantum Groups ◽  
Cartan Subalgebra ◽  
Positive Root ◽  
Point Of View ◽  
Root Space ◽  
Quantum Double ◽  
Braided Group ◽  
Negative Root ◽  
Quasitriangular Hopf Algebra

We introduce a quasitriangular Hopf algebra or ‘quantum group’ U(B), the double-bosonization, associated to every braided group B in the category of H-modules over a quasitriangular Hopf algebra H, such that B appears as the ‘positive root space’, H as the ‘Cartan subalgebra’ and the dual braided group B* as the ‘negative root space’ of U(B). The choice B=Uq(n+) recovers Lusztig's construction of Uq(g); other choices give more novel quantum groups. As an application, our construction provides a canonical way of building up quantum groups from smaller ones by repeatedly extending their positive and negative root spaces by linear braided groups; we explicitly construct Uq(sl3) from Uq(sl2) by this method, extending it by the quantum-braided plane. We provide a fundamental representation of U(B) in B. A projection from the quantum double, a theory of double biproducts and a Tannaka–Krein reconstruction point of view are also provided.

scholarly journals Probing quantum gravity effects with quantum mechanical oscillators

2020 ◽  
Vol 74 (9) ◽  
Author(s):  
Michele Bonaldi ◽  
Antonio Borrielli ◽  
Avishek Chowdhury ◽  
Gianni Di Giuseppe ◽  
Wenlin Li ◽  
...  
Keyword(s):  
Quantum Gravity ◽  
Quantum Physics ◽  
Deformation Parameter ◽  
Thermal State ◽  
Classical Trajectory ◽  
Point Of View ◽  
Gravity Models ◽  
Gravity Effects ◽  
The Status ◽  
Mechanical Oscillators

Abstract Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization. Graphical abstract

scholarly journals Quantum Determinism of Relative Spacetime Counting

2020 ◽  
Author(s):  
Eugene Machusky ◽  
Ljubov Lisovska ◽  
Olexander Goncharov
Keyword(s):  
Functional Analysis ◽  
Communication Systems ◽  
High Speed ◽  
Quantum Physics ◽  
Maximum Level ◽  
Point Of View ◽  
Engineering Practice ◽  
Simple Explanation ◽  
Computational Accuracy ◽  
Quantum Calculus

The phenomenal mathematical efficiency of quantum field theories in modern high-speed information and communication systems has a very simple explanation from the point of view of common sense and higher mathematical logic: all of them – quantum cosmology, quantum physics, quantum metrics and quantum calculus – are the self-informational mathematical systems based on symbolic and numerical functional analysis and elementary recursive calculations of interrelated space and time parameters of matter motion in various states of the material environment.For the first time in scientific and engineering practice, it was clearly shown that the information entropy of both standard symbolic and non-standard numerical functional analysis has absolute exact limits of computational accuracy – 1/10^16 and 1/10^64, respectively. Moreover, the second limit determines the maximum level of accuracy of practical quantum metrics and calculations and fully coordinates four branches of classical physics – thermodynamics, electrodynamics, gravidynamics, chromodynamics with special and general relativity.

scholarly journals Local quantum physics and models

1993 ◽  
Vol 155 (1) ◽  
pp. 199-204 ◽  
Author(s):  
Rudolf Haag
Keyword(s):  
Quantum Physics ◽  
Local Quantum
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