Related papers: Quantization of systems with temporally varying di…
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Inspired by theories such as Loop Quantum Gravity, a class of stochastic graph dynamics was studied in an attempt to gain a better understanding of discrete relational systems under the influence of local dynamics. Unlabeled graphs in a…
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong…
Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a…
A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principal function which generates canonical time evolution and ensures…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
We show that probability is locally conserved in discrete time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any…
We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form…
To solve the path integral for quantum gravity, one needs to regularise the space-times that are summed over. This regularisation usually is a discretisation, which makes it necessary to give up some paradigms or symmetries of continuum…
The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time…
Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a…