Related papers: Relational time in generally covariant quantum sys…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
The problem of time evolution in quantum cosmology is studied in the context of a dust-filled, spatially flat Friedmann-Robertson-Walker universe. In this model, two versions of the commonly-adopted notion of internal time can be…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…
We study the relation between two evolution pictures that are currently considered for totally constrained theories. Both descriptions are based on Rovelli's evolving constants approach, where one identifies a (possibly local) degree of…
We show that generalizations of classical and quantum dynamics with two times lead to fundamentally constrained evolution. At the level of classical physics, Newton's second law is extended and exactly integrated in $1+2$ dimensional space,…
We have previously shown (arXiv:1912.00033) that three approaches to relational quantum dynamics -- relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations -- are equivalent. Here we show that this `trinity'…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
The implications of manifestly covariant formulation of relativistic quantum mechanics depending on a scalar evolution parameter, canonically conjugated to the variable mass, is still an unsettled issue. In this work we find a complete set…
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…
Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system…
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…
Quantile clocks are defined as convolutions of subordinators $L$, with quantile functions of positive random variables. We show that quantile clocks can be chosen to be strictly increasing and continuous and discuss their practical modeling…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
We study the quantum dynamics of a time reparametrization invariant system with a vanishing Hamiltonian. The evolution of the physical degrees of freedom of the system is described, both at the classical and at the quantum level, in…