Mathematica Applications for Tensor Analysis in Physics Classes

Hee-Joong Yun

Department of Optical & Electronic Physics
Mokwon University, S.KOREA

Abstract

Tensor calculations and manipulations are frequently required to treat physics problems in physics classes. Given that tensor analysis is considered difficult, physicists would like to avoid learning tensor analysis, even though the tensor is the most fundamental tool in physics. For the laws of physics are expressed in a manner that makes their invariance under the coordinate transformations manifest, it should be written in term of tensors.

Tensorial 3.0 package [R. Cabrera] we have used here enables one to calculate and manipulate easily with Mathematica, even for not in area of expertise.

The aim of this work is creating tensors from the formulas based on undergraduate-level course texts (J. B.Marion, Classical dynamics and J. R.Reitz et al., Foundation of electromagnetic theory) and a graduate-level text(J. D.Jackson, Classical electrodynamics) to manipulate tensor analysis to gain deeper insights into the physics. The Mathematica simulations creating or transforming  the tensors, including the quadrupole moment tensor, the inertia tensor in a three-vector space, and the antisymmetric electromagnetic field tensor in Minkowski space, are shown. They will enhance the capabilities of students and researchers in tensor analysis and comprehension to the elegant features of this complicated physics structure. Also shown is how to gain the components of the electromagnetic field tensor and coordinate the transformation to get a dual field tensor from which to obtain a Maxwell’s equation in tensor form. This work in Mathematica reveals the need for the tensor calculation in the quadrupole moment tensor and shows that tensor analysis can be performed quickly and without tedium.