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We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into…
We discuss an approach to quantum gerbes over quantum groups in terms of q-deformation of transition functions for a loop group bundle. The case of the quantum group SUq(2) is treated in some detail.
It is shown that equations describing the Galilean electromagnetism in the presence of sources hold invariant under the l-conformal Galilei group for an arbitrary (half)integer parameter l. The group contains transformations which link an…
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…
We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory…
A fundamental question in the field of quantum reference frames concerns what global properties of a system can be determined by observers operating entirely from within that system. We investigate this question by extending both the…
The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval --…
This paper proposes an intrinsic or background-independent quantum framework based on entangled state rather than absolute quantum state, it describes a quantum relative state between the under-study quantum system and the quantum measuring…
This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…
Consider a locally compact quantum group $\mathbb{G}$ with a closed classical abelian subgroup $\Gamma$ equipped with a $2$-cocycle $\Psi:\hat{\Gamma}\times\hat{\Gamma}\to\mathbb{C}$. We study in detail the associated Rieffel deformation…
We present a group of transformations in the quantum configuration space of loop quantum gravity that contains the set of all transformations generated by the flux variables.
We study Heisenberg's uncertainty relation relative to a quantum reference frame (QRF). We introduce the QRF as a covariant phase-space observable, show that when described relative to it, position and momentum appear compatible, and derive…
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of…
A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type…
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…
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,…
The quantum deformation concept is applied to a study of isovector pairing correlations in nuclei of the mass 40<A<100 region. While the non-deformed (q -> 1) limit of the theory provides a reasonable global estimate for strength parameters…