New Fundamental Dynamical Equation for Higher Derivative Quantum Field Theories

article distributed under the Creative Commons Attribution License, which permits unre-stricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In space-time with the Minkowski metric, the group of the metric is the inhomogeneous Lorentz group, which is also known as the Poincaré group. A dynamical equation is called fundamental if it is invariant with respect to the group of the metric, which consists of all transformations that leave the metric invariant. A method based on this group is used to derive two infinite sets of Poincare ́ invariant linear dynamical equations for scalar and analytical functions that represent free, spin-zero, massive elementary particles. The sets contain two different types of fundamen-tal higher derivative dynamical equations, which are used to construct higher derivative quantum field theories. One of these sets contains the original Klein-Gordon equation and it is shown that all physicall