Symbolic studies of Maxwell’s equations in space-time algebra formalism

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Abstract

Different implementations of Clifford algebra: spinors, quaternions, and geometric algebra, are used to describe physical and technical systems. The geometric algebra formalism is a relatively new approach, destined to be used primarily by engineers and applied researchers. In a number of works, the authors examined the implementation of the geometric algebra formalism for computer algebra systems. In this article, the authors extend elliptic geometric algebra to hyperbolic space-time algebra. The results are illustrated by different representations of Maxwell’s equations. Using a computer algebra system, Maxwell’s vacuum equations in the space-time algebra representation are converted to Maxwell’s equations in vector formalism. In addition to practical application, the authors would like to draw attention to the didactic significance of these studies.

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A. V. Korol’kova

RUDN University

Author for correspondence.
Email: korolkova-av@rudn.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198

M. N. Gevorkyan

RUDN University

Email: gevorkyan-mn@rudn.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198

A. V. Fedorov

RUDN University

Email: 1042210107@rudn.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198

K. A. Shtepa

RUDN University

Email: 1042210111@pfur.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198

D. S. Kulyabov

RUDN University; Joint Institute for Nuclear Research

Email: kulyabov-ds@rudn.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198; Dubna, Moscow oblast, 141980

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