Related papers: Geometric Quantization and Epistemically Restricte…
A new set of twisted geometric variables is introduced to parametrize the holonomy-flux phase space in loop quantum gravity. It is verified that these new geometric variables, after symplectic reduction with respect to the Gauss constraint,…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
We introduce a category composed of all quantizations of all Poisson algebras. By the category, we can treat in a unified way the various quantizations for all Poisson algebras and develop a new classical limit formulation. This formulation…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized…
We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
Recently, it has been observed that a certain class of classical theories with constraints can be quantized by a mathematical procedure known as Rieffel induction. After a short exposition of this idea, we apply the new quantization theory…
In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev invariants. In this paper we introduce the Hamiltonian…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the…
We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a space of wavefunctions based on the Vassiliev knot invariants.…
We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
We address one of the open problems in quantization theory recently listed by Rieffel. By developping in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict, flabby quantization,…