Introduction
The field in mathematics may include scalar field, vector field, tensor field in general relativity, spinor field of particles, torsion and twistor fields, etc [1].
Torsion field calls also as spin field or axion field. It is the field produced by the object spin angular momentum distorting the space-time coordinates. In 1913 E.J. Cartan declared that there must be a field produced by rotation in nature. In general relativity, Einstein assumed that the torsion field did not exist, but in 1922 Cartan first considered the distortion of the object spin in space-time, thus generating the torsion field, and supplement to a more complete relativity. Weyl pointed out also in the 1930s that mathematics could not exclude the torsion field, which is another force, for the fifth force. In the 1970s a new field of physics was formed: Einstein-Cartan theory as the basis of torsion field, whose primary source is the rotations of the elementary particle. Rotation is everywhere, and each rotation element produces its own torsion field. These fields consisting of elementary particles, atoms, molecules, people, planets, etc., fuse in the universe. P. Bridgman established that the torsion field can be generated not only by the proper rotational moment of the elementary particle, called spin, but also under certain conditions, especially when the structure of the physical vacuum is distorted. These form different torsion fields.
Russian scientists developed torsion theory and some practical execution. A. Akimov proposed that torsion may be divided into static and dynamic field. The static torsion field is generated by a rotating object with a constant angular velocity, which does not radiate energy. But, if a rotating object has more than one form of motion, then it releases energy in the form of a dynamic torsion field wave. Further, Akimov developed his communication concept by torsion field. G. Shipov combined the concept of Cartan and the research of Akimov, and developed the theory of physical vacuum in 1998.
Some scientists believe that torsion field is a front of science in the 21st century. Of course, Weinberg also disagreed [2]. Although there are differences, exploration papers are still many, in 2025 Pylypovskyi, et al., studied the effects of magnetic frustration in ferrotoroidal spin chains via curvature and torsion [3]. Rodriguez-Benites, et al., investigated the cosmological dynamics of a homogeneous scalar field nonminimally coupled to torsion gravity, which also interacts with cold dark matter through energy and momentum transfer [4]. In this paper, we discuss theories and applications of torsion field, and propose some new methods.