Related papers: Quantum Reference Frames and Quantum Transformatio…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
The quantum space-time model which accounts material Reference Frames (RF) quantum effects considered for flat space-time and ADM canonical gravity. As was shown by Aharonov for RF - free material object its c.m. nonrelativistic motion in…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…
We define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We establish a criterion for the classical…
In this survey, we relate frame theory and quantum information theory, focusing on quantum 2-designs. These are arrangements of weighted subspaces which are in a specific sense optimal for quantum state tomography. After a brief…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
If several interventions performed on a quantum system are localized in mutually space-like regions, they will be recorded as a sequence of ``quantum jumps'' in one Lorentz frame, and as a different sequence of jumps in another Lorentz…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
An experiment to test for relativistic frame dragging effects with quantum interferometry is proposed. The idea that the classical trajectories of the interferometer surround a spherical mass source whose angular momentum is perpendicular…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
The quantum mechanics of a simple mechanical system is considered. A group of gears can serve as a model for several different systems such as an artifically constructed nanomechanical device or a group of ring molecules. It is shown that…
Successful applications of a conceptually novel setup of Quantum Field Theory, that accounts for all subtheories of the Standard Model (QED, Electroweak Interaction and Higgs, Yang-Mills and QCD) and beyond (Helicity 2), call for a…
Quantum descriptions of polarization show the rich degrees of freedom underlying classical light. While changes in polarization of light are well-described classically, a full quantum description of polarimetry, which characterizes…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…