Related papers: Functional evolution of scalar fields in bounded o…
Interacting quantum fields on spacetimes containing regions of closed timelike curves (CTCs) are subject to a non-unitary evolution $X$. Recently, a prescription has been proposed, which restores unitarity of the evolution by modifying the…
We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of…
Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined…
Motivated by the possibility to use Bose-Einstein condensates as quantum simulators for spacetime curvature, we study a massless relativistic scalar quantum field in spatially curved Friedmann-Lema\^itre-Robertson-Walker universes with…
In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary,…
Process of formation of the universe with its further expansion in the first evolution stage is investigated in the framework of Friedmann-Robertson-Walker metrics on the basis of quantum model, where a new type of matter is introduced,…
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can…
In the present article we study the cosmological evolution of a two-scalar field gravitational theory defined in the Jordan frame. Specifically, we assume one of the scalar fields to be minimally coupled to gravity, while the second field…
This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquenss and stability for classical solutions is provided. We study also the associated dual Cauchy…
Motion in bounded domains represents a paradigm in several settings: from billiard dynamics, to random walks in a finite lattice, with applications to relevant physical, ecological and biological problems. A remarkable universal property,…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…
We apply a very simple procedure to construct non-singular cosmological models for flat Friedmann universes filled with minimally coupled scalar fields or by tachyon Born-Infeld-type fields. Remarkably, for the minimally coupled scalar…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb…
We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in --either a background or effective-- spacetime with spatial sections of flat compact…
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in…
We study a first-order formulation for the coupled evolution of a quantum scalar field and a classical Friedmann universe. The model is defined by a state dependent hamiltonian constraint and the time dependent Schr\"odinger equation for…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…