Related papers: Covariant localizations in the torus and the phase…
In the recent article Phys. Rev. D 100, no. 4, 043533 (2019) a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…
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…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
Combining elements of twistor-space, phase space and Clifford algebras, we propose a framework for the construction and quantization of certain (quadric) varieties described by Lorentz-covariant multivector coordiantes. The correspondent…
The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
The effects of a beamsplitter are frequently described mathematically as a matrix acting on a two input ports vector. This might be comprehensive for a scalar field but certainly insufficient in case of photons which are vector fields. In…
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…
A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the…
We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…
We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton operators is also given. From the Hamilton operators we…
Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal…
We show that local Lorentz covariance arises canonically as the group of transformations between local thermal states in the framework of Local Quantum Physics, given the following three postulates: (i) Local observable algebras are…