Related papers: Path Integral Quantization of Cosmological Perturb…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…
Contents: Introduction. The Present State of the Universe. What Can We Expect From a Complete Cosmological Theory? An Overview of Quantum Effects in Cosmology. Parametric (Superadiabatic) Amplification of Classical Waves. Graviton Creation…
We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
One possible description of the very early stages of the evolution of the universe is provided by Chaotic Inflationary Cosmology. For that model the role of the inflaton field is played by quantum gravitational effects. We study if such a…
After a brief summary of general relativity and cosmology, we present the basic concepts underlying inflation, the currently best motivated models for the early Universe. We describe the simplest inflation models, based on a single scalar…
The Hamiltonian counterpart of classical Lagrangian field theory is covariant Hamiltonian field theory where momenta correspond to derivatives of fields with respect to all world coordinates. In particular, classical Lagrangian and…
Using a scheme proposed earlier we set up Hamiltonian path integral quantization for a particle in two dimensions in plane polar coordinates.This scheme uses the classical Hamiltonian, without any $O(\hbar^2)$ terms, in the polar…
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role…
We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein-Hilbert action in $d > 2$ dimensions. We show that this is inequivalent to what is obtained from…
We explain in detail the quantum-to-classical transition for the cosmological perturbations using only the standard rules of quantum mechanics: the Schrodinger equation and Born's rule applied to a subsystem. We show that the conditioned,…
In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signal that can be observed. Beyond the spatial distributions of astronomical objects, the spatial…
We present a covariant formulation for constructing general quadratic actions for cosmological perturbations, invariant under a given set of gauge symmetries for a given field content. This approach allows us to analyse scalar, vector and…
We quantize to completion an inflationary universe with small inhomogeneities in the framework of loop quantum cosmology. The homogeneous setting consists of a massive scalar field propagating in a closed, homogeneous scenario. We provide a…
The path integral of the relativistic Coulomb system is solved, and the wave functions are extracted from the resulting amplitude.
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
In the first quantised description of strings, we integrate over target space co-ordinates $X^\mu$ and world sheet metrics $g_{\alpha\beta}$. Such path integrals give scattering amplitudes between the `in' and `out' vacuua for a…
Perturbations in a universe with matter and cosmological constant are computed in terms of the primordial scalar perturbation up to second order. The calculation is easy -- a generalization of the spherical dust solution. Our expression…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is…