It is well known that quantization cannot increase the Kullback-Leibler divergence which can be thought of as the first moment of the log-likelihood ratios. In this paper, this result is extended to the case of second and higher moments of the log-likelihood ratios. It is shown that quantization may result in an increase of the second or higher moments of the log-likelihood ratio, but such an i...

We construct the quadratic analogue of the boson Fock functor. While in the first order (linear) case all contractions on the 1–particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e. the contractions), all the gauge transformation...

In this paper, the problem of distributed adaptive consensus tracking control for second-order nonlinear heterogeneous multi-agent systems (MASs) with input quantization is considered. A output feedback scheme based on a K-filter developed to suppress influences unknown disturbances and quantization. contrast existing approaches, an additional design parameter introduced into controller ensure ...

A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism and improvements sophisticated theory are touching briefly, all “salient points theory”. The unfamiliar reader can consider this as a “soft” introduction to topic.

Notwithstanding known obstructions to this idea, we formulate an attempt to turn quantization into a functorial procedure. We define a category Poisson of Poisson manifolds, whose objects are integrable Poisson manifolds and whose arrows are isomorphism classes of regular Weinstein dual pairs; it follows that identity arrows are symplectic groupoids, and that two objects are isomorphic in Poiss...

The understanding of the meaning of quantization seems to be the main problem in understanding quantum structures. In this paper first the difference between quantized particle vs. radiation fields in the formalism of canonical quantization is discussed. Next von Weizsäcker’s concept of ”multiple quantization” which leads to an understanding of quantization as an iteration of probability theory...

3 Kinetic exchange 7 3.1 A toy model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Direct exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Second quantization for pedestrians . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 Mean-field treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.5 Superexchange...

We outline the principal results of a recent examination of the quantization of systems with firstand second-class constraints from the point of view of coherent-state phase-space path integration. Two examples serve to illustrate the procedures.

Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold independent vacuum Einstein gravitational field dynamics. The arguments carry also mutatis mutandis to the case of fr...