The state estimation of a quantized system (Q.S.) is a challenging problem for designing feedback control and model-based fault diagnosis algorithms. The core of a Q.S. is a continuous variable system whose inputs and outputs are represented by their corresponding quantized values. This paper concerns with state estimation of a Q.S. by a qualitative observer. The presented observer in this pape...

We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures larger than the chemical potential. In a second part, using a lattice model for the quantum field, we explain how to carefully generalize the usual Bogoliubov a...

Coideal subalgebras of the quantized enveloping algebra are surveyed, with selected proofs included. The first half of the paper studies generators, Harish-Chandra modules, and associated quantum homogeneous spaces. The second half discusses various well known quantum coideal subalgebras and the implications of the abstract theory on these examples. The focus is on the locally finite part of th...

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As appli...

We introduce a new renormalization for the powers of the Dirac delta function. We show that this new renormalization leads to a second quantized version of the Virasoro sector w∞ of the extended conformal algebra with infinite symmetries W∞ of Conformal Field Theory ( [4]-[7], [11], [13], [14]). In particular we construct a white noise (boson) representation of the w∞ generators and commutation...

We analyze if entangled fermionic states can be described by a projector in the one-particle Hilbert space. A method is developed for realizing entanglement and general second quantized fermionic and bosonic fields in the framework of the fermionic projector. Our constructions are discussed with regard to decoherence phenomena and the measurement problem.

This paper is partly a report on current knowledge concerning the structure of (generic) quantized coordinate rings and their prime spectra, and partly propaganda in support of the conjecture that since these algebras share many common properties, there must be a common basis on which to treat them. The rst part of the paper is expository. We survey a number of classes of quantized coordinate r...