Related papers: Recent Progress in Regge Calculus
A discretized version of canonical gravity in (3+1)-d introduced in a previous paper is further developed, introducing the Liouville form and the Poisson brackets, and studying them in detail in an explicit parametrization that shows the…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
We give a generally covariant description, in the sense of symplectic geometry, of gauge transformations in Batalin-Vilkovisky quantization. Gauge transformations exist not only at the classical level, but also at the quantum level, where…
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of…
We discuss the relation between spacetime diffeomorphisms and gauge transformations in theories of the Yang-Mills type coupled with Einstein's General Relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of…
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
This paper generalizes our previous paper on the discrete Schwarzschild type solution in the Regge calculus, the simplicial electrodynamics earlier considered in the literature is incorporated in the case of the presence of a charge.…
Theory of gravity is considered in the Regge-Teitelboim approach in which the pseudo-Riemannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of…
The space of all Riemannian metrics is infinite-dimensional. Nevertheless a great deal of usual Riemannian geometry can be carried over. The superspace of all Riemannian metrics shall be endowed with a class of Riemannian metrics; their…
We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime…
In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove…
This is a summary talk covering recent progress in perturbative methods for gauge theories and gravity, applications of AdS/CFT duality, vacuum energy, and string theory models of particle physics and cosmology.
The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in Regge Calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical…
We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show…
A hybrid model which allows to interpolate between the (original) Regge approach and dynamical triangulations is introduced. The gained flexibility in the measure is exploited to study dynamical triangulation in a fixed geometry. Our…
Encountered in the literature generalisations of general relativity to independent area variables are considered, the discrete (generalised Regge calculus) and continuum ones. The generalised Regge calculus can be either with purely area…
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.…
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and…
The gauge symmetry is said unfree if the gauge transformation leaves the action functional unchanged provided for the gauge parameters are constrained by the system of partial differential equations. The best known example of this…