Related papers: Generalized Bundle Quantum Mechanics
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
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…
An algebraic structure underlying the quantity calculus is proposed consisting in an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them…
Applications to quantum gravity of some results in C*-algebras are developed. We open by describing why algebra may be an integral aspect of quantum gravity. By interpreting the inner automorphisms of a C*-algebra as families of parallel…
In this paper, algebroid bundle associated to affine metrics provide an structure for unification of gravity and electromagnetism and, geometrization of matter.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
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 propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…
Theories based on General Relativity or Quantum Mechanics have taken a leading position in macroscopic and microscopic Physics, but fail when used in the other extremity. Thus, we try to establish a new structure of united theory based on…
Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the…
A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
This paper formulates a generalization of our work on quantum knots to explain how to make quantum versions of algebraic, combinatorial and topological structures. We include a description of previous work on the construction of Hilbert…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…