Directly Interacting Massless Particles - a Twistor Approach

Twistor phase spaces are used to provide a general description of the dynamics of a finite number of directly interacting massless spinning particles forming a closed relativistic massive and spinning system with an internal structure. A Poincare invariant canonical quantization of the so obtained twistor phase space dynamics is performed.Comment: LaTeX, approx. 16 pages; to appear in Journal of Mathematical Physics, March or April 1996 issu

Negative forms and path space forms

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.Comment: 12 pp.; the Introduction has been rewritten and mention of cohomology dropped in Proposition 3.2; material slightly reorganize

Twistors, special relativity, conformal symmetry and minimal coupling - a review

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincare scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled, Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so called Thomas Bergman Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything else in the papper) on page 23 delete

Application of Discrete Differential Forms to Spherically Symmetric Systems in General Relativity

In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method is mainly its manifest coordinate independence. Three numerical schemes are introduced, the results of which are compared with the corresponding analytic solutions. The error of two schemes converges quadratically to zero. For one scheme the errors depend strongly on the initial data.Comment: 22 pages, 6 figures, accepted by Class. Quant. Gra

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

Covariance properties and regularization of conserved currents in tetrad gravity

We discuss the properties of the gravitational energy-momentum 3-form within the tetrad formulation of general relativity theory. We derive the covariance properties of the quantities describing the energy-momentum content under Lorentz transformations of the tetrad. As an application, we consider the computation of the total energy (mass) of some exact solutions of Einstein's general relativity theory which describe compact sources with asymptotically flat spacetime geometry. As it is known, depending on the choice of tetrad frame, the formal total integral for such configurations may diverge. We propose a natural regularization method which yields finite values for the total energy-momentum of the system and demonstrate how it works on a number of explicit examples.Comment: 36 pages, Revtex, no figures; small changes, published versio

On certain quasi-local spin-angular momentum expressions for small spheres

The Ludvigsen-Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius $r$ about a point $o$. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common leading term is of order $r^4$, and it is the product of the contraction of the energy-momentum tensor and an average of the approximate boost-rotation Killing vector that vanishes at $o$ and of the 3-volume of the ball of radius $r$. In vacuum spacetimes the leading term is of order $r^6$, and the factor of proportionality is the contraction of the Bel-Robinson tensor and an other average of the same approximate boost-rotation Killing vector.Comment: 16 pages, Plain Te