Related papers: Quantum Dimensions and Quantum Galois Theory
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…
A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible…
The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional…
The fusion rules of the 2-permutation orbifold of an arbitrary lattice vertex operator algebra are determined by using the theory of quantum dimension.
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Based on a clear ontology of material individuals, we analyze in detail the factual semantics of quantum theory, and argue that the basic mathematical formalism of quantum theory is just okay with (a certain form of ) realism and that it is…
The algebras obtained as fixed points of the action of the cyclic group $Z_N$ on the coordinate algebra of the quantum disc are studied. These can be understood as coordinate algebras of quantum or non-commutative cones. The following…
We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
Recently it has been proposed, using the formalism of positive-operator-valued measures, a possible definition of quantum coordinates for events in the context of quantum mechanics. In this short note we analyze this definition from the…
We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…