Related papers: Hilbert space structure in quantum gravity: an alg…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
$SU(\infty)-QGR$ is a foundationally quantum approach to cosmology and gravity. It assumes that the Hilbert space of the Universe as a whole represents the symmetry group $SU(\infty)$, and demonstrates this symmetry for Hilbert spaces of…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix $\{\hg_{ab}(x)\}$ composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
In the general setting of quantum controls, it is unrealistic to control all of the degrees of freedom of a quantum system. We consider a scenario where our direct access is restricted to a small subsystem $S$ that is constantly interacting…
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since…
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…