Explanation of parity nonconservation.

Space inversion and other discrete symmetries are treated within the frame of a theory of fundamental forces based only on general considerations of causality, symmetry, and stability, without ad hoc differential equations. The basic space-time M is the Einstein universe R(1) x S(3) as a causal (or conformal) rather than a pseudo-Riemannian manifold. Its connected symmetry group is then a 15-parameter group G locally equivalent to SO(2, 4), while the isometry group K of the Einstein universe is a 7-parameter subgroup.

Covariant chronogeometry and extreme distances: Elementary particles.

We study a variant of elementary particle theory in which Minkowski space, M(0), is replaced by a natural alternative, the unique four-dimensional manifold M with comparable properties of causality and symmetry. Free particles are considered to be associated (i) with positive-energy representations in bundles of prescribed spin over M of the group of causality-preserving transformations on M (or its mass-conserving subgroup) and (ii) with corresponding wave equations. In this study these bundles, representations, and equations are detailed, and some of their basic features are developed in the cases of spins 0 and (1/2).

Symmetry and causality properties of physical fields.

Representations of groups of causality-preserving transformations on locally Minkowskian space-times, by actions on classes of wave functions of designated transformation properties, are analyzed, in extension of the conventional theoretical treatment of free relativistic particles. In particular, the constraints of positivity of the energy and finiteness of propagation velocity are developed, and the concept of mass is explored, within the indicated framework.