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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…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
Consideration of the geometric quantization of the phase space of a particle in an external Yang-Mills field allows the results of the Mackey-Isham quantization procedure for homogeneous configuration spaces to be reinterpreted. In…
In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
We consider questions related to quantizing complex valued functions defined on a locally compact topological group. In the case of bounded functions, we generalize R. Werner's approach to prove the characterization of the associated normal…
We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
This paper is one of a series of papers on coherent spaces and their applications, defined in the recent book 'Coherent Quantum Mechanics' by the first author. The paper studies coherent quantization -- the way operators in the quantum…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate…
Based on a more careful canonical analysis, we motivate a reduced quantization - in the sense of superspace quantization - of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
We define covariantly a deformation of a given algebra, then we will see how it can be related to a deformation quantization of a class of observables in Quantum Field Theory. Then we will investigate the operator order related to this…
We investigate an entangled deformation of the deterministic quantum cloning process, called enscription, that can be applied to (certain) sets of distinct quantum states which are not necessarily orthogonal, called texts. Some basic…
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3 \equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient isotopic…
We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by Wang. More precisely, the resulting quantum groups…
We built up a explicit realization of (0+1)-dimensional q-deformed superspace coordinates as operators on standard superspace. A q-generalization of supersymmetric transformations is obtained, enabling us to introduce scalar superfields and…