Related papers: Time dependent perturbation theory from Wheeler De…
We compare two versions of deformed dispersion relations (energy vs momenta and momenta vs energy) and the corresponding time delay up to the second order accuracy in the quantum gravity scale (deformation parameter). A general framework…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
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…
In this work, we show that a gauge-theoretic description of Jackiw-Teitelboim (JT) gravity naturally yields a Henneaux-Teitelboim (HT) unimodular gravity via a central extension of its isometry group, valid for both flat and curved…
One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field…
We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries…
We investigate three aspects of the supposed problem of time: The disagreement between the treatments of time in general relativity and quantum theory, the problem of recovering time from within an isolated Universe and the prevalence of a…
The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
Using Hamilton-Jacobi theory, we develop a formalism for solving semi-classical cosmological perturbations which does not require an explicit choice of time-hypersurface. The Hamilton-Jacobi equation for gravity interacting with matter…
Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage…
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…
We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in…
The recent transition from decelerated to accelerated expansion can be seen as a reflection (or "bounce") in the connection variable, defined by the inverse comoving Hubble length ($b=\dot a$, on-shell). We study the quantum cosmology of…
The time dependent quantum variational principle is emerging as an important means of studying quantum dynamics, particularly in early universe scenarios. To date all investigations have worked within a Gaussian framework. Here we present…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like…
We consider a simplified model of quantum gravity using a mini-superspace description of an isotropic and homogeneous universe with dust. We derive the corresponding Friedmann equations for the scale factor, which now contain a dependence…
We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak…