Circuit Theory Based on New Concepts and Its Application to Quantum Theory 38. Heaviside: Founder of Complex Function Theory Derived from Elliptic Functions

Heaviside reformulated the Maxwell equations (P. J. Nahin: OLIVER HEAVISIDE, The Johns Hopkins University Press, 2002). The vector analysis based on the quaternions defined by Hamilton was employed as the analytical method to derive the Poynting vector in the reformulation. However, the treatment of quaternions became invalid once the Poynting vector was obtained with the reformulation. Instead, Heaviside's analytical method has been switched to vector analysis using complex numbers (based on Euler's formula). This method is considered to have contributed significant development to modern mathematics and is also considered to be a problem-posing question that is comparable to “Hilbert's 23 Problems". In this Session, we will present one solution to this problem by applying the quaternions defined by Pauli.