Related papers: Quantum Gravity on a Manifold with boundaries: Sch…
The coupling of the metric to an incoherent dust introduces into spacetime a privileged dynamical reference frame and time foliation. The comoving coordinates of the dust particles and the proper time along the dust worldlines become…
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…
A covariant Hamiltonian description of Palatini's gravity on manifolds with boundary is presented. Palatini's gravity appears as a gauge theory satisfying a constraint in a certain topological limit. This approach allows the consideration…
We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…
We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field.…
In this paper, we shall present a new equation of motion with Quantum effect in spacetime. To do so, we propose a classical-quantum duality. We also generalize the Schordinger equation to the spacetime and obtain a relativistic wave…
A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by…
We provide a generating functional for the gravitational field, associated to the relaxation of the primary constraints as extended to the quantum sector. This requirement of the theory, relies on the assumption that a suitable time…
S. Weinberg pointed out a way to introduce a cosmological term by modifying the theory of gravity. This modification would be justified if the Einstein equations with the cosmological term could be obtained in the classical limit of some…
The wave-function in quantum gravity is supposed to obey the Wheeler-DeWitt (WDW) equation, however there is neither a satisfactory probability interpretation nor a successful solution to the problem of time in the WDW framework. To gain…
Exact solution of the Schr\"{o}dinger equation is given for a particle inside a hard sphere whose wall is moving with a constant velocity. Numerical computations are presented for both contracting and expanding spheres. The propagator is…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…
The problem of time in canonical quantum gravity remains one of the most significant challenges, primarily due to the "frozen" formalism emerging from the Wheeler-DeWitt equation. Within the ADM formalism, we introduce a novel approach in…
The path integral of 4D Einstein-Hilbert gravity for the de Sitter-like Universe with fluctuations is investigated, and the transition amplitude from one boundary configuration to another is computed. The gravitational system is described…
In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space"…
We consider RFDiff invariant Horava-Lifshitz gravity action with additional Lagrange multiplier term that is a function of scalar curvature. We find its Hamiltonian formulation and we show that the constraint structure implies the same…
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…
The wave function of quantum mechanics is not a boost invariant and gauge invariant quantity. Correspondingly, reference frame dependence and gauge dependence are inherited to most of the elements of the usual formulation of quantum…