  This research establishes an operational measurement way to express the
quantum field theory in a geometrical form. In four-dimensional spacetime
continuum, the orthogonal rotation is defined. It forms two sets of equations:
one set is geometrical equations, another set is the motion equations. The
Lorentz transformation can be directly derived from the geometrical equations,
and the proper time of general relativity is well expressed by time
displacement field. By the motion equations, the typical time displacement
field of matter motion is discussed. The research shows that the quantum field
theory can be established based on the concept of orthogonal rotation. On this
sense, the quantum matter motion in physics is viewed as the orthogonal
rotation of spacetime continuum. In this paper, it shows that there are three
typical quantum solutions. One is particle-like solution, one is
generation-type solution, and one is pure wave type solution. For each typical
solution, the force fields are different. Many features of quantum field can be
well explained by this theoretic form. Finally, the general matter motion is
discussed, the main conclusions are: (1). Geometrically, cosmic vacuum field
can be described by the curvature spacetime; (2). The spatial deformation of
planet is related with a planet electromagnetic field; (3). For electric charge
less matter, the volume of matter will be expanding infinitely; (4).For strong
electric charge matter, it shows that the volume of matter will be contracting
infinitely.
