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 R1 × S3 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. Correlation with conventional relativistic theory is based on a canonical imbedding of Minkowski space M0 into ˜M, together with the unique extendability of all transformations of the scaling-extended Poincaré group ˜P from M0 to global transformations on ˜M. The fundamental fermion field F and boson field B are here restricted to be real and are fully invariant under ˜Ge, where the superscript e denotes the inclusion of space and time inversions. The role of C on F is taken over by a real matrix having the eigenvalues ±i, that commutes with ˜G but anticommutes with space inversion. The spin space for B consists of the real linear transformations on that for F. There is a corresponding natural total Lagrangian that is both ˜Ge and O(2)-gauge invariant, the latter leading to lepton and baryon number conservation, and which is nonparametric except for scale. The Weyl and Maxwell equations are deduced, and compelling identifications made for neutrinos and the photon. The e and μ neutrino pairs occur in strikingly inequivalent positions in F, appearing symmetric only in the conventional relativistic limit R → ∞, where R is the (˜G-invariant) fundamental length interpretable as the radius of the space S3. The photon occurs as the lowest member of a coherent subfamily of B that includes natural candidates for bare versions of the W and Z particles. In the relativistic limit the interaction Lagrangian becomes a sum over all elementary processes, one of which appears as quantum electrodynamics with Majorana-type electrons.

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