Related papers: Particles on a Circle in Canonical Lineal Gravity
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories,…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
We construct a limit of Hamiltonian gravity as the determinant of the spatial triad (and hence of the four-metric) goes to zero. Within the Barbero-Immirzi SU (2) formulation, we present two possible realizations of this limit, with the…
We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The…
The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its…
The article is a natural continuation of the papers by Gavrilov and Gitman (Class.Quant.Grav. {\bf 17} (2000) L133; Int. J. Mod. Phys. A15 (2000) 4499) devoted to relativistic particle quantization. Here we generalize the problem,…
The effects of physical interactions are usually incorporated into the quantum theory by including the corresponding terms in the Hamiltonian. Here we consider the effects of including the gravitational potential energy of massive particles…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…
We present the Hamiltonian formulation of a relativistic point-particle coupled to Einstein gravity and its canonical quantization \`a la Wheeler-DeWitt. In the resulting quantum theory, the wave functional is a function of the particle…
We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is…
It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group.…
We derive, in 2+1 dimensions, classical solutions for metric and motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the $N$-body static case, and are perturbative in…
Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri…
Building on the relativistic Hamiltonian of Sonnleitner and Barnett arXiv:1806.00234 and its post-Newtonian extensions by Schwartz and Giuilini arXiv:1908.06929, we investigate composite atomic systems in dynamical gravitational…
Forces parallel to particle trajectories occur in physically meaningful situations, including relativistic cosmology and Einstein frame scalar-tensor gravity. These situations have Newtonian analogues that we discuss to provide intuition…
This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…