相关论文: Recent Mathematical Developments in Quantum Genera…
The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems,…
This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
Over the last few years part of the quantum-gravity community has adopted a more optimistic attitude toward the possibility of finding experimental contexts providing insight on non-classical properties of spacetime. I review those…
I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances.…
We argue for enlarging the traditional view of quantum gravity, based on "quantizing GR", to include explicitly the non-spatiotemporal nature of the fundamental building blocks suggested by several modern quantum gravity approaches (and…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
The construction of a continuum limit for the dynamics of loop quantum gravity is unavoidable to complete the theory. We explain that such a construction is equivalent to obtaining the continuum physical Hilbert space, which encodes the…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
The canonical quantum theory of gravity -- Quantum Geometrodynamics (QG) is applied to the homogeneous Bianchi type IX cosmological model. As a result, the framework for the quantum theory of homogeneous cosmologies is developed. We show…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full space-time covariance to spatial diffeomorphism invariance yields a non-vanishing Hamiltonian, a resolution of the `problem of time', and…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…