Related papers: Perfect discretization of reparametrization invari…
The issue of local gauge invariance in the simplicial lattice formulation of gravity is examined. We exhibit explicitly, both in the weak field expansion about flat space, and subsequently for arbitrarily triangulated background manifolds,…
When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path…
We present evidence that there is a 4D model that satisfies the conditions of renormalizability and diffeomorphism invariance simultaneously at the 2-loop level. The traceless mode is treated perturbatively, while the conformal mode can be…
A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular,…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
I give a resolution of the conformal mode divergence in the Euclidean gravitational path-integral by isolating the trace of the diffeomorphisms and its contribution to the Faddeev-Popov measure.
We consider the application of the consistent lattice quantum gravity approach we introduced recently to the situation of a Friedmann cosmology and also to Bianchi cosmological models. This allows us to work out in detail the computations…
We study the issue of diffeomorphism symmetry in group field theories (GFT), using the recently introduced noncommutative metric representation. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties…
The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) \otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of…
In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field…
After an overview of variational principles for discrete gravity, and on the basis of the approach to conformal transformations in a simplicial PL setting proposed by Luo and Glickenstein, we present at a heuristic level an improved scheme…
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…
The paper is the second part of the work devoted to the problem of time in quantum cosmology. Here we consider in detail two approaches within the scope of Feynman path integration scheme: The first, by Simeone and collaborators, is…
We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
We define the idea of {\it real path quantum theory}, a realist generalisation of quantum theory in which it is postulated that the configuration space path actually followed by a closed quantum system is probabilistically chosen. This is…
The key ingredient for lattice regularized quantum gravity is diffeomorphism symmetry. We formulate a lattice functional integral for quantum gravity in terms of fermions. This allows for a diffeomorphism invariant functional measure and…