Related papers: Quantum general invariance and loop gravity
Decoherence may not solve all of the measurement problems of quantum mechanics. It is proposed that a solution to these problems may be to allow that superpositions describe physically real systems in the following sense. Each quantum…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
A local conception is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties --- as e.g. vacuum catastrophe --- of the global approach.
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general…
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map.…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of…
Many homogeneous, four-dimensional space-time geometries can be considered within real projective geometry, which yields a mathematically well-defined framework for their deformations and limits without the appearance of singularities.…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
The history of general relativity suggests that in absence of experimental data, constructing a theory on philosophical first principles can lead to a very useful theory as well as to ground-breaking insights about physical reality. The two…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
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…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…