Related papers: Deformation Quantization: Twenty Years After
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $\sigma =d^{2}/2$. One suggests a new general method of the…
We study the geometric quantization process for twisted Poisson manifolds. First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for twisted Poisson manifolds and we use it in order to characterize their prequantization…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…
In this paper Quantum Mechanics with Fundamental Length is chosen as the theory for describing the early Universe. This is possible due to the presence in the theory of General Uncertainty Relations from which unavoidable it follows that in…
The conventional interpretation of quantum mechanics, though it permits a correspondence to classical physics, leaves the exact mechanism of transition unclear. Though this was only of philosophical importance throughout the twentieth…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
In this paper a new approach to investigation of Quantum and Statistical Mechanics of the Early Universe (Planck scale) - density matrix deformation - is proposed. The deformation is understood as an extension of a particular theory by…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
Firstly we discuss different versions of noncommutative space-time and corresponding appearance of quantum space-time groups. Further we consider the relation between quantum deformations of relativistic symmetries and so-called doubly…
The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie…
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…
This set of notes corresponds to a mini-course given in September 2018 in Bedlewo; it does not contain any new result; it complements -- with intersection -- the introduction to formal deformation quantization and group actions,…
Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed…
The subject of this study is Quantum and Statistical Mechanics of the Early Universe. In it a new approach to investigation of these two theories - density matrix deformation - is proposed. The distinguishing feature of the proposed…