Creating and Transforming a Second-Rank Antisymmetric Field-Strength Tensor Fαβ in Minkowski Space using MATHEMATICA

Abstract

As the laws of physics are expressed in a manner that makes their invariance under coordinate transformations manifest, they should be written in terms of tensors. Furthermore, tensors make manifest the characteristics and behaviors of electromagnetic fields through inhomogeneous, anisotropic, and compressible media. Electromagnetic fields are expressed completely in tensor form, Fαβ, which implies both electric field E → and magnetic field B → rather than separately in the vector fields. This study presents the Mathematica platform that generates and transforms a second-rank antisymmetric field-strength tensor Fαβ and whiskbroom pattern in Minkowski space. The platforms enhance the capabilities of students and researchers in tensor analysis and improves comprehension of the elegant features of complete structure in physics.