Related papers: Presymplectic Geometry and the Problem of Time. Pa…
We develop a systematic Hamiltonian formulation for a gravitating topological matter system in three-dimensional spacetime, coupling a scalar gauge field and a rank-2 antisymmetric gauge field to Einstein--Cartan gravity. We perform the…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric…
These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the…
We will present a consistent description of Hamiltonian dynamics on the ``symplectic extended phase space'' that is analogous to that of a time-\underline{in}dependent Hamiltonian system on the conventional symplectic phase space. The…
The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ of an event space $Y$. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The…
We describe the symplectic reduction construction for the physical phase space in gauge theory and apply it for the BF theory. Symplectic reduction theorem allows us to rewrite the same phase space as a quotient by the gauge group action,…
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…
The Hamiltonian formalism of the generalized unimodular gravity theory, which was recently suggested as a model of dark energy, is shown to be a complicated example of constrained dynamical system. The set of its canonical constraints has a…
Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full space-time covariance to spatial diffeomorphism invariance yields a non-vanishing Hamiltonian, a resolution of the `problem of time', and…
This thesis investigates how the metric and tetrad formulations of three gravitational field theories in manifolds with timelike boundaries within the covariant phase space program. With the recently developed relative bicomplex framework,…
The conventional spacetime formulation of general relativity may be recast as a dynamics of spatial 3-geometries (geometrodynamics). Furthermore, geometrodynamics can be derived from first principles. I investigate two distinct sets of…
Finite dimensional models that mimic the constraint structure of Einstein's General Relativity are quantized in the framework of BRST and Dirac's canonical formalisms. The first system to be studied is one featuring a constraint quadratic…
We show the existence of a time-space noncommutativity (NC) for the physical system of a massive relativistic particle by exploiting the underlying symmetry properties of this system. The space-space NC is eliminated by the consideration of…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
We show that the diffeomorphisms of an extended phase space with time, energy, momentum and position degrees of freedom that leave invariant the symplectic 2-form and and a degenerate orthogonal metric dt^2 locally satisfy Hamilton's…
The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly…