Theory of Equations. By J. V. Uspensky. Pp. vii, 353. 27s. 1948. (McGraw-Hill)

In the past decade, the understanding of the dynamics of small molecules in intense laser fields has advanced enormously. At the same time, the technology of ultra-short pulsed lasers has equally progressed to such an extent that femtosecond lasers are now widely available. This review is written from an experimentalist's point of view and begins by discussing the value of this research and defining the meaning of the word 'intense'. It continues with describing the Ti: sapphire laser, including topics such as pulse compression, chirped pulse amplification, optical parametric amplification, laser-pulse diagnostics and the absolute phase. Further aspects include focusing, the focal volume effect and space charge. The discussion of physics begins with the Keldysh parameter and the three regimes of ionization, i.e. multi-photon, tunnelling and over-the-barrier. Direct-double ionization (non-sequential ionization), high-harmonic generation, above-threshold ionization and attosecond pulses are briefly mentioned. Subsequently, a theoretical calculation, which solves the time-dependent Schrodinger equation, is compared with an experimental result. The dynamics of H-2(+) in an intense laser field is interpreted in terms of bond-softening, vibrational trapping (bond-hardening), below-threshold dissociation and laser-induced alignment of the molecular axis. The final section discusses the modified Franck-Condon principle, enhanced ionization at critical distances and Coulomb explosion of diatomic and triatomic molecules.

https://iopscience.iop.org/article/10.1088/0034-4885/67/5/R01/pdf

The dynamics of small molecules in intense laser fields

The present status of the quasi-local mass-energy-momentum and angular momentum constructions in general relativity is reviewed. First the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities are recalled. Then the various specific constructions and their properties (both successes and defects) are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned. This review is based on the talks given at the Erwin Schrodinger Institute, Vienna, in July 1997, at the Universitat Tubingen, in May 1998, and at the National Center for Theoretical Sciences in Hsinchu and at the National Central University, Chungli, Taiwan, in July 2000.

/pdf/quasi-local-energy-momentum-and-angular-momentum-in-gr-a-2ickuhcmd5.pdf

Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article

The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.

/pdf/quasi-local-energy-momentum-and-angular-momentum-in-general-wmf4x6598j.pdf

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity.

https://www.luth.obspm.fr/~luthier/gourgoulhon/pdf/GourgJ06a.pdf

A 3+1 perspective on null hypersurfaces and isolated horizons

A covariant 2 + 2 formalism is developed in which space-time is decomposed into a family of spacelike two-surfaces and their orthogonal timelike two-surface elements. The resulting 2 + 2 breakup of the Einstein vacuum field equations is then used to investigate covariant formulations of spacelike, characteristic, and mixed initial-value problems. In each case the so-called conformal two-structure (essentially the conformal metric of a family of spacelike two-surfaces) is identified as the freely specifiable initial data. The formalism makes clear the geometrical significance of both the initial data and the various choices of gauge variables. A Lagrangian formulation is included which supports the role of the conformal two-structure as dynamical variables of the pure gravitational field.

Covariant 2+2 formulation of the initial-value problem in general relativity

This is the first in a series of papers concerning a project to set up a computer database of exact solutions in general relativity which can be accessed and updated by the user community. In this paper, we briefly discuss the Cartan-Karlhede invariant classification of geometries and the significance of the standard form of a spinor. We then present algorithms for putting the Weyl spinor, Ricci spinor and general spinors into standard form.

https://iopscience.iop.org/article/10.1088/0264-9381/17/3/306/pdf

Classifying geometries in general relativity: I. Standard forms for symmetric spinors

We derive a 2 t 2 formulation of Ashtekar variables, focusing on the important special case of a double null foliation of spacetime. The significance of the 2 + 2 formalism in general is that it isolates the me gravitational degrees of freedom. The derivation mirrors that of a recent paper by Coldberg PZ d in which Ashtekar's 3 t I canonical formulation of Einstein's theory of gravitation is reformulated in term of a time parameter whose level sets are null hypersurfaces. In this paper we restdct anention to the Lagrangian formulation. PACS numbers: 0420C

http://iopscience.iop.org/article/10.1088/0264-9381/12/3/013/pdf

2+2 decomposition of Ashtekar variables

This paper is part of a long term program to develop combined Cauchy and characteristic codes as investigative tools in numerical relativity. In the third stage attention is devoted to axisymmetric systems possessing two spatial degrees of freedom. In the second of two preliminary theoretical papers, the vacuum field equations for the characteristic region are obtained and the compactified equations are regularized.

Combining cauchy and characteristic codes IV: the characteristic field equations in axial symmetry

This is the third in a series of papers concerning a project to set up a computer database of exact solutions in general relativity which can be accessed and updated by the user community. In this paper, we describe how the Cartan-Karlhede method for classifying a geometry is accomplished in practice. We give as an example the classification of the Edgar-Lugwig conformally flat pure radiation metrics.

R. A. d'Inverno

Papers

Covariant 2+2 formulation of the initial-value problem in general relativity

Classifying geometries in general relativity: I. Standard forms for symmetric spinors

2+2 decomposition of Ashtekar variables

Combining cauchy and characteristic codes IV: the characteristic field equations in axial symmetry

Classifying geometries in general relativity: III. Classification in practice