Related papers: Wave Equations on Lorentzian Manifolds and Quantiz…
This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution,…
Numerical simulations of quantum field theories on lattices serve as a fundamental tool for studying the non-perturbative regime of the theories, where analytic tools often fall short. Challenges arise when one takes the continuum limit or…
These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…
The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level…
A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for…
The basic principles of generalization of the group theoretical approach to the relativistic wave equations on curved spaces are examined. The general method of the determination of wave equations from the known symmetry group of a…
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here…
These notes are self-contained, with the first 7 chapters used in a one-semester course with recommended texts by Wald, by Misner, Thorne and Wheeler, and by Schutz. In its treatment of topics covered in these standard texts, the…
Basic aspects of a program to put field theories quantized in radial coordinates on the lattice are presented. Only scalar fields are discussed. Simple examples are solved to illustrate the strategy when applied to the 3D Ising model.
An effective field theory framework is used to investigate some Lorentz-violating effects on the generation of electromagnetic and gravitational waves, complementing previous work on propagation. Specifically we find solutions to a…
We discuss how to fix the gauge in the canonical treatment of Lagrangians, with finite number of degrees of freedom, endowed with time reparametrization invariance. The motion can then be described by an effective Hamiltonian acting on the…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal…
We quantise and solve the dynamics of gravitational waves in a quantum Friedmann-Lemaitre-Robertson-Walker spacetime filled with perfect fluid. The classical model is formulated canonically. The Hamiltonian constraint is de-parametrised by…
This a book is for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, the elegant description…
We present a spinfoam formulation of Lorentzian quantum General Relativity. The theory is based on a simple generalization of an Euclidean model defined in terms of a field theory over a group. The model is an extension of a recently…
We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.