Related papers: That strange procedure called quantisation
In this work, we find the Poisson superalgebras related to schemes of quantization. Initially, we consider the Dirac superbracket in the context of the quantization of constrained systems. Next, we show the existence of a Poisson…
A class of stochastic processes, called "weak Dirichlet processes", is introduced and its properties are investigated in detail. This class is much larger than the class of Dirichlet processes. It is closed under C^1$-transformations and…
We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear…
A third quantization formalism is applied to a simplified multiverse scenario. A well defined quantum state of the multiverse is obtained which agrees with standard boundary condition proposals. These states are found to be squeezed, and…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
An extension of the Weyl-Wigner-Moyal formulation of quantum mechanics suitable for a Dirac quantized constrained system is proposed. In this formulation, quantum observables are described by equivalent classes of Weyl symbols. The Weyl…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
In this paper we explore the idea of looking at the Dirac quantisation conditions as $\hbar$-dependent constraints on the tangent bundle to phase-space. Starting from the path-integral version of classical mechanics and using the natural…
The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) K\"ahler manifold. The deformation quantisation for such systems is scetched resulting in the Wick-type symbols for the…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for this system is obtained. These constraint conditions are now allowed to depend not…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
A PhD student is locked inside a box, imitating a quantum system by mimicking the measurement statistics of any viable observable nominated by external observers. Inside a second box lies a genuine quantum system. Either box can be used to…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
We apply a new and mathematically rigorous method for the quantization of constrained systems to two-dimensional gauge theories. In this method, which quantizes Marsden-Weinstein symplectic reduction, the inner product on the physical state…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.
Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…