相关论文: Quantum Geometry and Gravity

Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…

The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…

After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…

The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…

Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…

General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…

We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…

In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…

We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory. The extended geometry distinguishes between the ordinary spacetime based…

Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…

We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the…

In this paper is considered a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics. This assumption can be interpreted as a transfer from the…

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…

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…

A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling…

In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…

Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…

We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…