Coordinate- and spacetime-independent quantum physics

The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a coordinate-frame-independent model of quantum particles within the framework of quantum field theory in curved spacetime. The aim of this article is to present a scalar-field-equation solution that is not only a zero-rank tensor under general coordinate transformations, but also common for anti-de-Sitter, de-Sitter, closed and open Einstein static universes. Moreover, it locally reduces to a Minkowski plane-wave solution and is non-perturbative in curvature. The former property makes it suitable for the standard applications of quantum theory in particle physics, while the latter allows then to gain insights into quantum physics in the strong-gravity regime.