Related papers: Canonical formulation and path integral for local …
A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…
The path-integral approach to cosmology consists in the computation of transition amplitudes between states of the quantum geometry of the universe. In the past, the concrete computation of these transitions amplitudes has been performed in…
We carry out the nonperturbative canonical quantization of several types of cosmological models that have already been studied in the geometrodynamic formulation using the complex path-integral approach. We establish a relation between the…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
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…
We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing…
We numerically study the Euclidean quantum cosmology of a closed, homogeneous and isotropic universe with a cosmological constant. A dust field acts as a clock, and we compute the ground state wavefunction, correlation function, and mean…
The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically…
Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy…
We outline the evaluation of the cosmological constant in the framework of the standard field-theoretical treatment of vacuum energy and discuss the relation between the vacuum energy problem and the gauge-group spontaneous symmetry…
The quantum theory of the Friedmann cosmological model with dust and cosmological constant ($\Lambda$) is not exactly solvable analytically. We apply Path Integral Monte Carlo (PIMC) techniques to study its quantum dynamics using the…
We develop the formalism for canonical reduction of $(1+1)$--dimensional gravity coupled with a set of point particles by eliminating constraints and imposing coordinate conditions. The formalism itself is quite analogous to the…
This article serves as a continuation for the discussion in arXiv:0911.3433, we analyze the invariance properties of the gravity path-integral measure derived from canonical framework, and discuss which path-integral formula may be employed…
A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are…
Canonical quantization of the Brane-World effective action presented by Kanno and Soda containing higher order curvature invariant terms, has been performed. It requires introduction of an auxiliary variable. As observed in a series of…
In a recent contribution we identified possible points of contact between the asymptotically safe and canonical approach to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of…
Quantum creation of the universe is described by the {\em density matrix} defined by the Euclidean path integral. This yields an ensemble of universes -- a cosmological landscape -- in a mixed quasi-thermal state which is shown to be…