We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields ϕ a , general Yukawa couplings and a 4 symmetry that forbids linear and trilinear terms in the scalar potential. Moreover, fermions become massive only after spontaneous symmetry breaking of the 4 symmetry by vacuum expectation values (VEVs) of the ϕ a . Introducing the shifted fields h a whose VEVs vanish, MS renormalization of the parameters of the unbroken theory suffices to make the theory finite. However, in this way, beyond tree level it is necessary to perform finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, in order to ensure vanishing one-point functions of the h a . Moreover, adapting the renormalization scheme to a situation with many scalars and VEVs, we consider the physical fermion and scalar masses as derived quantities, i.e. as functions of the coupling constants and VEVs. Consequently, the masses have to be computed order by order in a perturbative expansion. In this scheme we compute the selfenergies of fermions and bosons and show how to obtain the respective one-loop contributions to the tree-level masses. Furthermore, we discuss the modification of our results in the case of Dirac fermions and investigate, by way of an example, the effects of a flavour symmetry group. *

We investigate Palatini f (R, Lm, Rµν T µν ) modified theories of gravity wherein the metric and affine connection are treated as independent dynamical fields and the gravitational Lagrangian is made a function of the Ricci scalar R, the matter Lagrangian density Lm, and a "matter-curvature scalar" Rµν T µν . The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum dependent metric, related to the physical metric by a matrix transformation. Similar to metric f (R, T, Rµν T µν ) gravity, the field equations impose the nonconservation of the energy-momentum tensor, leading to an appearance of an extra force on massive test particles. We obtain the explicit form of the field equations for massive test particles in the case of a perfect fluid, and an expression for the extra force. The nontrivial modifications to scalar fields and both linear and nonlinear electrodynamics are also considered. Finally, we detail the conditions under which the present theory is equivalent to the Eddington-inspired Born-Infeld (EiBI) model.

No abstract

We study the field of an electric point charge that is slowly lowered into an n + 1 dimensional Schwarzschild-Tangherlini black hole. We find that if n > 3, then countably infinite nonzero multipole moments manifest to observers outside the event horizon as the charge falls in. This suggests the final state of the black hole is not characterized by a Reissner-Nordström-Tangherlini geometry. Instead, for odd n, the final state either possesses a degenerate horizon, undergoes a discontinuous topological transformation during the infall of the charge, or both. For even n, the final state is not guaranteed to be asymptotically-flat.

In this report we analyze a subset of chemical equations that have equal numbers of elements and unknown coefficients; linear algebraically, these relate to n X n matrix systems. Here we associate inhomogeneous eigenvector occurrences to structural properties of chemical equations.