A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the U4 theory of gravitation, predicts, in addition to the usual infinite-rhnge gravitational interaction mediated by the metric field, a new, very weak, spin contact interaction of gravitatiorial origin. %'e summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the U4 theory arises as a local gauge theory for the Poincare group in space-time. The deviations of the U" theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed. CONTENTS

We present an algorithm which enables us to state necessary and sufficient conditions for the solvability of generalized Hamilton-type equations of the form ι (X) ω=α on a presymplectic manifold (M,ω) where α is a closed 1-form. The algorithm is phrased in the context of global infinite-dimensional symplectic geometry, and generalizes as well as improves upon the local Dirac–Bergmann theory of constraints. The relation between our algorithm and the geometric constraint theory of Śniatycki, Tulczyjew, and Lichnerowicz is discussed.

Early energy-momentum investigations for gravitating systems gave reference frame dependent pseudotensors; later the quasilocal idea was developed. Quasilocal energy-momentum can be determined by the Hamiltonian boundary term, which also identifies the variables to be held fixed on the boundary. We show that a pseudotensor corresponds to a Hamiltonian boundary term. Hence they are quasilocal and acceptable; each is the energy-momentum density for a definite physical situation with certain boundary conditions. These conditions are identified for well-known pseudotensors. *

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