Related papers: The Modular Group, Operator Ordering, and Time in …
We study the operator formulation of classical mechanics by explicitly applying it to two central potentials in 2 dimensions. After constructing the classical Hamiltonian operators and corresponding Schr\"odinger like equations, we solve…
We consider the quantum partition function for a system of quantum spinors and then derive an equivalent (or dual) classical partition function for some scalar degrees of freedom. The coupling between scalars is non-trivial (e.g. a model on…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \cite{AGS}. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of…
In general relativity, time functions are crucial objects whose existence and properties are intimately tied to the causal structure of a spacetime and also to the initial value formulation of the Einstein equations. In this work we…
U(1) Chern-Simons theory is quantized canonically on manifolds of the form $M=\mathbb{R}\times\Sigma$, where $\Sigma$ is a closed orientable surface. In particular, we investigate the role of mapping class group of $\Sigma$ in the process…
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
We study the properties of a quantum field with time as a dynamical variable. Temporal vibrations are introduced to restore the symmetry between time and space in a matter field. The system with vibrations of matter in time and space obeys…
The Belinksy-Khalatnikov-Lifshitz dynamics of gravity close to a spacelike singularity can be mapped, at each point in space separately, onto the motion of a particle bouncing within half the fundamental domain of the modular group. We show…
Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
It has recently been shown by Goldberg et al that the holonomy group of the chiral spin-connection is preserved under time evolution in vacuum general relativity. Here, the underlying reason for the time-independence of the holonomy group…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
The two lineal gravities --- based on the de Sitter group or a central extension of the Poincar\'e group in 1+1 dimensions --- are shown to derive classically from a unique topological gauge theory. This one is obtained after a dimensional…
Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a…
We present a family of classical spacetimes in 2+1 dimensions. Such a spacetime is produced by a Nambu-Goto self-gravitating string. Due to the special properties of three-dimensional gravity, the metric is completely described as a…