相关论文: Spectral Geometry and Causality

General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…

A purely geometrical relativity theory results from a construction that produces from three-dimensional space a happy unification of Kaluza's five-dimensional theory and Weyl's conformal theory. The theory can provide geometrical…

We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop…

We investigate Lorentzian quantum gravity coupled to a template matter sector with gauge fields, scalars and fermions. In the absence of quantised gravity, the matter sector by itself is renormalisable, but UV-incomplete. Provided quantum…

Caianiello's derivation of Quantum Geometry through an isometric embedding of the spacetime ({\bf M},\tilde{g}) in the pseudo-Riemannian structure ({\bf T^*M},g^*_{AB}) is reconsidered. In the new derivation, a non-linear connection and the…

Some of the most outstanding questions in the field of gravitation and geometry remain unsolved as a result of our limited understanding of the global structure of the spacetime geometry and the role played by global spacetime…

In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded…

We argue that a consistent coupling of a quantum theory to gravity requires an extension of ordinary `first order' Riemannian geometry to second order Riemannian geometry, which incorporates both a line element and an area element. This…

Being able to perform explicit computations in a nonperturbative, Planckian regime is key to understanding quantum gravity as a fundamental theory of gravity and spacetime. Rather than a variety of different approaches to quantum gravity,…

Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe "before" the classical big bang is obtained…

It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…

We show how uncertainty in the causal structure of field theory is essentially inevitable when one includes quantum gravity. This includes the fact that lightcones are ill-defined in such a theory. This effect is small in the effective…

Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the…

We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime disappears, replacing it with a discrete approximation to the causal path space described as an object in a model category. One of…

The causal spacetimes admitting a covariantly constant null vector provide a connection between relativistic and non-relativistic physics. We explore this relationship in several directions. We start proving a formula which relates the…

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general…

This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path…

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…

Motivated by hints of the effective emergent nature of spacetime structure, we formulate a spacetime-free algebraic framework for quantum theory, in which no a priori background geometric structure is required. Such a framework is necessary…

We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…