Alena Tensor is a recently discovered class of energy-momentum tensors that provides a mathematical framework in which the description of a physical system in curved spacetime and its description in a flat spacetime with fields are equivalent. As demonstrated in previous publications, in curved spacetime this tensor reproduces Einstein Field Equations and in flat Minkowski spacetime, it describes physical system with fields that can be widely configured. Thanks to the obtained compliance with QM and QED, the use of the discussed tensor may significantly simplify Quantum Field Theory equations and a new interpretation of the Schrödinger equation is possible. In the article it has also been shown that the use of Alena Tensor for the electromagnetic field takes into account effects related to the particle's spin, Abraham–Lorentz effect and, in the curvilinear description, this excludes non-physical phenomena such as the black hole singularity. The article contains a method for verifying Alena Tensor within QM, proposing an explanation for the discrepancy between the Dirac and Klein-Gordon solutions. It also discusses prospects for the application of Alena Tensor in unification theories against the background of existing research directions.

By developing the previously proposed method of combining continuum mechanics with Einstein Field Equations, it has been shown that the classic relativistic description, curvilinear description, and quantum description of the physical system may be reconciled using the proposed Alena Tensor. For a system with an electromagnetic field, the Lagrangian density equal to the invariant of the electromagnetic field was obtained, vanishing four-divergence of canonical four-momentum appears to be consequence of the Poyinting theorem, and explicit form of one of gauges of the electromagnetic four-potential was introduced. The proposed method allows for further development with additional fields.

The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system with an electromagnetic field, leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress-energy tensor expresses relativistic Cauchy's momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.