A modification of Einstein-Schrodinger theory that contains Einstein-Maxwell-Yang-Mills theory

The Lambda-renormalized Einstein-Schrodinger theory is a modification of the original Einstein-Schrodinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein-Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of dxd Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein-Maxwell-Yang-Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein-Maxwell-Yang-Mills theory in that the extra terms in the field equations are 10^-13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg-Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.Comment: latex2e, generalized from U(1)xSU(2) to U(1)xSU(d

An investigation of the spin structure of the proton in deep inelastic scattering of polarised muons on polarised protons

Ashman J, Badelek B, Baum G, et al. An investigation of the spin structure of the proton in deep inelastic scattering of polarised muons on polarised protons. Nucl.Phys. B. 1989;328(1):1-35

Extreme events in population dynamics with functional carrying capacity

A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations between populations can be realized not merely through direct interactions, as in the usual predator-prey Lotka-Volterra model, but also through the influence of species on the carrying capacities of each other. This includes the self-influence of each kind of species on its own carrying capacity with delays. Several examples of such evolution equations with functional carrying capacities are analyzed. The emphasis is given on the conditions under which the solutions to the equations display extreme events, such as finite-time death and finite-time singularity. Any destructive action of populations, whether on their own carrying capacity or on the carrying capacities of co-existing species, can lead to the instability of the whole population that is revealed in the form of the appearance of extreme events, finite-time extinctions or booms followed by crashes.Comment: Latex file, 60 pages, 24 figure