Related papers: A trick for passing degenerate points in Ashtekar …
We study decompositions of the global NVALUE constraint. Our main contribution is theoretical: we show that there are propagators for global constraints like NVALUE which decomposition can simulate with the same time complexity but with a…
We describe the main ingredients needed to create, from the smooth lagrangian density, a variational principle for discrete motions of a discrete rod, with corresponding conserved Noether currents. We describe all geometrical objects in…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
We revisit the Kodama state by quantizing the theory of General Relativity (GR) with dynamical Chern-Simons (dCS) gravity. We find a new exact solution to the Wheeler-DeWitt equation where the Pontryagin term induces a modification in the…
The methods of dynamical systems have found wide applications in cosmology, with focus either upon inflation or upon the passage into dark energy era. In this paper, we endeavor to capture the whole history of the universe into a dynamical…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
We present a broad and simple class of scalar-tensor scenarios that successfully realize dynamical damping of the effective cosmological constant, therefore providing a viable dynamical solution to the fine-tuning or "old" cosmological…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
We prove that projectivity is an open condition for deformations of algebraic spaces with rational singularities. V.2: references updated and corrected.
If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…
In this paper, we consider a fully-discrete approximation of an abstract evolution equation deploying a non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the…
We show how a deformed composition law of four-momenta can be used to define, at the classical level, a modified notion of spacetime for a system of two particles through the crossing of worldlines in particle interactions. We present a…
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into…
We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained…
Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The…
We consider the algebra of spatial diffeomorphisms and gauge transformations in the canonical formalism of General Relativity in the Ashtekar and ADM variables. Modifying the Poisson bracket by including surface terms in accordance with our…
We use the jump problem technique developed in a recent paper by Grushevsky, Krichever and the second author to compute the variational formula of any stable differential and its periods to arbitrary precision in plumbing coordinates. In…
We give an SU(2) covariant representation of the constraints of Euclidean general relativity in the Ashtekar variables. The guiding principle is the use of triads to transform all free spatial indices into SU(2) indices. A central role is…
In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that…