Journal ArticleDOI
Squeezing Bogoliubov transformations on the infinite mode CCR‐algebra
Reads0
Chats0
TLDR
A detailed analysis of and a general decomposition theorem for in general unbounded symplectic transformations on an arbitrary complex pre-Hilbert space (one-boson test function space) are given in this article.Abstract:
A detailed analysis of and a general decomposition theorem for in general unbounded symplectic transformations on an arbitrary complex pre‐Hilbert space (one–boson test function space) are given. The structure of strongly continuous symplectic groups on such spaces is determined. The connection between quadratic Hamiltonians, Bogoliubov transformations, and symplectic transformations is discussed in the Fock representation, and their relevance for squeezing operations in quantum optics is pointed out. The results for this rather general class of transformations are proved in a self‐contained fashion.read more
Citations
More filters
Journal ArticleDOI
Functional evolution of free quantum fields
TL;DR: In this paper, the authors consider the problem of evolving the state of a quantum field between any two (in general, curved) Cauchy surfaces and show that functional evolution of the quantum state can be satisfactorily described using algebraic quantum field theory.
Journal ArticleDOI
Hybrid quantization of an inflationary model: The flat case
TL;DR: In this paper, a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations is presented, in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus.
Journal ArticleDOI
Quantum Gowdy T3 model: a uniqueness result
TL;DR: In this paper, it was shown that the chosen Fock quantization is in fact unique up to unitary equivalence if one demands unitary implementation of the dynamics and invariance under the group of S translations.
Journal ArticleDOI
Quantum Gowdy T 3 model: A unitary description
TL;DR: In this article, a canonical analysis of the family of linearly polarized Gowdy spacetimes is presented, in which the true degrees of freedom are described by a scalar field that satisfies a Klein-Gordon type equation in a fiducial time-dependent background.
Journal ArticleDOI
Unique Fock quantization of scalar cosmological perturbations
TL;DR: In this article, the authors investigated the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lema-tre-Robertson-Walker model with a massive scalar field as matter content.
References
More filters
Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
A Course in Functional Analysis
TL;DR: In this article, an introductory text in functional analysis aimed at the graduate student with a firm background in integration and measure theory is presented, which helps the student to develop an intuitive feel for the subject.