相关论文: General Frame Structures On Quantum Principal Bund…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…
A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is non-fixed. In quantum theory non-fixed quantities are subject to quantum uncertainty. It is…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
In this paper it is shown that the structure of the configuration space of any continua is what is called in differential geometry a {\it principle bundle} \cite{Frankel2011ThePhysics}. A principal bundle is a structure in which all points…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
We construct a noncommutative geometry with generalised `tangent bundle' from Fell bundle $C^*$-categories ($E$) beginning by replacing pair groupoid objects (points) with objects in $E$. This provides a categorification of a certain class…
This note presents a simple and unified formulation of the most fundamental structures used in quantum information with qubits, arbitrary dimension qudits, and quantum continuous variables. This \emph{general quantum variables} construction…
It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…
We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle…
Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…
Many bundle gerbes constructed in practice are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stevenson proved that gerbes on simply-connected manifolds,…
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…
A common feature of the extended phase space of gauge theory, the crossed product of quantum theory, and quantum reference frames (QRFs) is the adjoining of degrees of freedom followed by a constraining procedure for the resulting total…
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame.…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…
In this paper we generalize special geometry to arbitrary signatures in target space. We formulate the definitions in a precise mathematical setting and give a translation to the coordinate formalism used in physics. For the projective…
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
In this manuscript, we will discuss the construction of covariant derivative operator in quantum gravity. We will find it is more perceptive to use affine connections more general than metric compatible connections in quantum gravity. We…