*-Quantizations of Fourier–Mukai Transforms

Quantizations of IR

Quantum real numbers are proposed by performing a quantum deformation of the standard real numbers IR. We start with the q-deformed Heisenberg algebra L̂q which is obtained by the Moyal ∗-deformation of the Heisenberg algebra generated by a and a. By representing L̂q as the algebras of q-differentiable functions, we derive quantum real lines from the base spaces of these functional algebras. We f...

Representations of Quantizations

1.1. Algebra case. Let A be a filtered quantization of a Z-graded finitely generated Poisson algebra A. By A -mod we denote the category of finitely generated A-modules. A basic tool to study such modules is to reduce them to finitely generated A-modules that can be studied by means of Commutative algebra/ Algebraic geometry. Given an A-module M , one introduces the notion of a good filtration ...

Quantizations of braided differential operators

Tracking Using Multilevel Quantizations

Most object tracking methods only exploit a single quantization of an image space: pixels, superpixels, or bounding boxes, each of which has advantages and disadvantages. It is highly unlikely that a common optimal quantization level, suitable for tracking all objects in all environments, exists. We therefore propose a hierarchical appearance representation model for tracking, based on a graphi...

Inequivalent Quantizations of Gauge Theories

It is known that the quantization of a system defined on a topologically non-trivial configuration space is ambiguous in that many inequivalent quantum systems are possible. This is the case for multiply connected spaces as well as for coset spaces. Recently, a new framework for these inequivalent quantizations approach has been proposed by McMullan and Tsutsui, which is based on a generalized ...