Recent zbMATH articles in MSC 20C35https://www.zbmath.org/atom/cc/20C352021-05-28T16:06:00+00:00WerkzeugThe coset space of the unified field theory.https://www.zbmath.org/1459.810802021-05-28T16:06:00+00:00"Davis, Simon"https://www.zbmath.org/authors/?q=ai:davis.simon-brianSummary: The coset space of the unified field theory is postulated, based on the automorphism group of the spinor space, which has been determined to be a direct sum as a result of the unitarity of the CKM matrix. Reduction sequences are considered, particularly in connection with vector bosons of the strong interactions and the six-dimensional theory yielding the Weinberg-Salam model upon integration over \(S^2\). The embedding of the manifold in a twelve-dimensional unified theory is established, and a solution to the field equations with a given form of the Ricci tensor is found. A coset space space \(\frac{G_2\times \mathrm{SU}(2)\times \mathrm{U}(1)}{\mathrm{SU}(3)\times \mathrm{U}(1)'\times \mathrm{U}(1)''}\) satisfying the holonomy condition for the Ricci tensor derived from the spinor equations is either nonsupersymmetric or admits a maximal \(N = 1\) supersymmetry. The greater weighting of a compactification of the reduced ten-dimensional theory over \(G_2/\mathrm{SU}(3)\) is verified, confirming the relevance of the elementary particle interactions.