Related papers: Path Integral Quantization of Cosmological Perturb…
We derive a Hamiltonian formulation of the theory of gauge invariant, linear perturbations in anisotropic Bianchi I spacetimes, and describe how to quantize this system. The matter content is assumed to be a minimally coupled scalar field…
The path integral for space-time noncommutative theory is formulated by means of Schwinger's action principle which is based on the equations of motion and a suitable ansatz of asymptotic conditions. The resulting path integral has…
This is a review on cosmological perturbation theory. After an introduction, it presents the problem of gauge transformation. Gauge invariant variables are introduced and the Einstein and conservation equations are written in terms of these…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…
The next decade will feature an abundance of novel cosmological data, while many fundamental questions about inflation remain. Given this, there is ample need for maximally efficient calculations, especially in non-standard scenarios for…
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
A global phase time is identified for homogeneous and isotropic cosmological models yielding from the low energy effective action of closed bosonic string theory. When the Hamiltonian constraint allows for the existence of an intrinsic…
Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant…
Calculations of the evolution of cosmological perturbations generally involve solution of a large number of coupled differential equations to describe the evolution of the multipole moments of the distribution of photon intensities and…
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different…
We generalise Langlois' Hamiltonian treatment of gauge-invariant linear cosmological perturbations to a cosmological setting with multiple scalar fields minimally coupled to gravity. We review the Hamilton-Jacobi-like technique for a…
Partial transport barriers in the chaotic sea of Hamiltonian systems influence classical transport, as they allow for a small flux between chaotic phase-space regions only. We establish for higher-dimensional systems that quantum transport…
We have found that the hierarchial problems appearing in cosmology is a manifestation of the quantum nature of the universe. The universe is still described by the same formulae that once hold at Planck's time. The universe is found to be…
In this paper we present the study of the scalar cosmological perturbations of a single field inflationary model up to first order in deviation. The Christoffel symbols and the tensorial quantities are calculated explicitly in function of…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
I investigate a new idea of perturbation theory in covariant canonical quantization. I present preliminary results for a toy model of a harmonic oscillator with a quartic perturbation, and show that this method reproduces the quantized…