abstract

The Einstein vacuum field equations are represented as a system of the first-order equations with the quadratic nonlinearity in field functions. Different variants of these equations are investigated, in particular the system of equations permitting the Lagrangian formulation. This method leads to the energy-momentum pseudotensor of the gravitational field which equals to the half-sum of the Einstein pseudotensor and the Maller–Mitskiévič pseudotensor.

abstract

Will man Quantentheorie in gekrümmten Räumen treiben, so braucht man Lösungen der Gleichung \([\gamma _{\mu },\gamma _{nu}]^+ = 2{\rm g}_{\mu \nu }\) Für ein beliebiges vorgebbares metrisches Tensorfeld werden eine hochdimensionale Lösung sowie eine allgemeinkovariante Tetradenlösung obiger Vertauschungsregeln angegeben.

abstract

All metrics on the Poincaré group which arc forminvariant under transformations of the relativistic symmetry as well as spatial rotations of a basis attached to the particle are found. The Lagrangian formalism for classical fields on P is developed and applied to the abelian gauge field, It is shown that in a particular choice of metric the gauge field has a neutral, massive and \(1^-\) component in addition to the usual electromagnetic field.

abstract

The reaction \(\pi {\rm d} \to \pi {\mit \Delta \Delta }\) is analysed from the point of view of a \({\mit \Delta \Delta }\) admixture to the deuteron ground state wave function. A simplified Glauber model approach is used to obtain \(\sigma (\pi {\rm d} \to \pi {\mit \Delta \Delta }) = 0.3~\mu \)b. This value has been calculated for 21 GeV/\(c\) incident pions but it is not sensitive to the primary pion energy.

abstract

Using the uncorrelated cluster emission as a model for non-diffractive processes, the diffractive production is estimated. Multiplicity and leading particle distributions in diffraction dissociation arc discussed. The cross-section for diffractive production is calculated and appears consistent with the data.

abstract

From an exposure of the 30-inch deuterium bubble chamber at Fermilab we examine 7600 events with \(\geq 3\) charged prongs. Multiplicity distributions for \(\pi ^+\)n, pn, and pd collisions are presented and are in general agreement with those expected based on knowledge of \(\pi ^-\)p and pp collisions at the same energy. The pd distribution is slightly wider than expected from a combination of free pp and pn collisions, and we estimate from this that the fraction of double inelastic collisions is about 5%. From the fraction of events with spectator protons we find that in about 15% of the inelastic break-up collisions both nucleons participate. We find no significant \(N\)-dependence in the double interaction effects so that the odd-prong multiplicities we present should correspond closely to free pn and \(\pi ^+\)n collisions. An interpretation of these results is suggested.

abstract

Sum rules for the \(I = 1\) P-wave \(\pi \pi \) scattering length \(a^1_{\rm P}\) are derived for the modulus and inverse of the scattering amplitude. These non-linear dispersive sum rules depend crucially on the positivity of the amplitudes’ imaginary part. Numerical examples are given which seem to prefer larger values of \(a^1_{\rm P}\). Comparison is made to the commonly used relations for \(a^1_{\rm P}\).