We study the Euler-Heisenberg gravity equations in the presence of a background scalar field through the perspective of the Riemannian Euler-Heisenberg gravity. We derive the Euler-Heisenberg equations in the picture of the Riemannian Euler-Heisenberg gravity.
We describe a monopole calculus for the Higgs mechanism. It is shown that the Higgs mechanism is the monopole of the Higgs field theory in the Higgs space. We also show that the Higgs mechanism can be eliminated in the quantum chromodynamics by a method similar to the Higgs model.