Affiliations: Louisiana Accelerator Center, Physics Department, Louisiana University at Lafayette, Lafayette, LA, USA
Correspondence:
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Corresponding author: Alexander D. Dymnikov, Louisiana Accelerator Center/Physics Dept/, Louisiana University at Lafayette, 320 Cajundome Blvd., Lafayette, LA 70506, USA. Tel.: +1 337 482 1845; Fax: +1 337 482 6190; E-mail: [email protected].
Abstract: A matrix theory of n-dimensional mathematical field and the motion of mathematical points in n-dimensional metric space is developed. Two spaces are considered: the n-dimensional space of an integrable coordinate vector {x} with the integrable metric g(x) and the n-dimensional space of a non-integrable but differentiable coordinate vector {Q}, where dQ=edx, dτ2=dQ˜dQ=dx˜g(x)dx, g(x)=e˜e, ∂(Q)=e−1∂(x). We call the coordinate space of the vector Q as the absolute space. The derivatives of the non-integrable but differentiable matrix e are expressed through the elements of the Christoffel symbols and the elements of the Ricci and Riemann curvature matrices. The absolute velocity vector u(Q)≡dQ/dτ and the absolute mathematical field matrix P≡u(Q)∂˜(Q) are introduced. We obtain two groups of the matrix field equations, the first of which is written in the two following forms: ∂(Q)P−P˜∂(Q)=ρu(Q), Ku(Q)=ρu(Q), where P the trace of the matrix P, K is is the absolute Ricci matrix function, u(Q) is the n-dimensional absolute velocity vector, ρ is a scalar function, which is the eigenvalue of K with the corresponding eigenvector u(Q). The interpretation of this pure mathematical theory in 4-dimensional space is the theory of the electromagnetic and gravitational fields and the motion of charged and neutral particles in the electromagnetic-gravitational field.
Keywords: Alternative theory of gravitation, gravitational field, electromagnetic field, motion of planets
