Related papers: Geometric Quantization and Epistemically Restricte…
We obtain a condensed reconstruction of algebraic quantum theory, emphasizing its foundational aspects and algebraic structure. We obtain the $W^*$-algebra structure from elementary assumptions about observers and how they can observe…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question,…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
Motivated by the invariance of current representations of quantum gravity under diffeomorphisms much more general than isometries, the Haag-Kastler setting is extended to manifolds without metric background structure. First, the causal…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
In the book [4] the general problem of reconstructing the Hilbert space formulation in quantum theory is discussed from the point of view of what I called conceptual variables, any variables defined by a person or by a group of persons.…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…
The incompatibility between the treatment of time in the classical and in the quantum theory results in the so-called problem of time in canonical quantum gravity. For this reason, attempts have been made to devise algorithms of…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We modify the Hochschild $\phi$-map to construct central extensions of a restricted Lie algebra. Such central extension gives rise to a group scheme which leads to a geometric construction of unrestricted representations. For a classical…
The paper provides an introduction into p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-Mechanics naturally provides a common ground for several different…
In this paper, we introduce C*-algebraic partial compact quantum groups, which are quantizations of topological groupoids with discrete object set and compact morphism spaces. These C*-algebraic partial compact quantum groups are…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…