Related papers: Quantum Dimensions and Quantum Galois Theory
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches…
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 determine explicit quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centers and block diagonal forms {of these algebras.} In the case where $q$ is {an arbitrary} root of unity, this further…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its…
We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum…
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
The characterization of physical systems requires a comprehensive understanding of quantum effects. One aspect is a proper quantification of the strength of such quantum phenomena. Here, a general convex ordering of quantum states will be…