Related papers: Quantization of dynamical symplectic reduction
The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…
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…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
A commonly adopted relational account of time evolution in generally-covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock…
One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
Quantum cosmology describes universe as a relativistic object with an evolution defined by an equation for the energy density corresponding to the least action principle: (Taganov, 2008). In quantum cosmology this equation plays the same…
A common feature of reparametrization invariant theories is the difficulty involved in identifying an appropriate evolution parameter and in constructing a Hilbert space on states. Two well known examples of such theories are the…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
In this essay, we argue that the problem of time should not be regarded as an issue to be resolved within the prevailing framework for studying quantum gravity, but rather as an indication that there is an issue within the framework itself.…
The recent suggestion that late time quantum dynamics may be important for resolving cosmological issues associated with our observed universe requires a consideration of several subtle issues associated with quantum cosmology, as we…
In this article I study how the problem of time of canonical approaches to quantum gravity affects the simple minisuperspace models used in quantum cosmology. I follow some authors who have argued that this issue makes the quantization of…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…