Related papers: Time evolution of Hamiltonian constraint system: a…

The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…

We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…

It is an intriguing question how local time can be introduced in the emergent picture of spacetime. In this paper, this problem is discussed in the context of tensor models. To consistently incorporate local time into tensor models, a rank-…

Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to…

We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

We study embedding gravity, a modified theory of gravity, in which our space-time is assumed to be a four-dimensional surface in flat ten-dimensional space. Based on a simple geometric idea, this theory can be reformulated as General…

Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…

A long-standing problem in quantum gravity and cosmology is the quantization of systems in which time evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented,…

This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…

Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…

The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated…

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. In this way, a physical clock with discrete…

The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are…

In this paper we introduce a definition of time that emerges in terms of the geometry of the configuration space of a dynamical system. We illustrate this, using the Hamilton-Jacobi equation, in various examples: particle mechanics on a…

By allowing for non zero vacuum expectation values for some of the fields that appear in the Hamiltonian constraint of canonical general relativity a time variable, with usual properties, can be identified; the constraint plays the role of…

A canonical formalism of the rank-three tensor model with the notion of local time is proposed. The consistency of the local time evolution is guaranteed by imposing that local Hamiltonians and the so(N) kinematical symmetry of the tensor…

For any Dirac theory of quantum gravity governed by a set of well-defined quantum constraints, we discover a universal formula for the exact form of the evolution Hamiltonian operator in a variable quantum reference frame of our…

Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…