An Alternative Approach for Solving Maxwell Equations
POLITECNICO DI TORINO (ITALY)
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At present the use of hypercomplex methods is pursued by a growing number of mathematicians, physicists and engineers. Quaternionic and Clifford calculus will be applied on wide classes of problems in very different fields of science. We explain Maxwell equations within the geometric algebras of real and complex quaternions. The connection between Maxwell equations and the Dirac equation will be elaborated. Using the Teodorescu transform we will deduce an iteration procedure for solving weak time-dependent Maxwell equations in isotropic homogeneous media. Assuming the so-called Drude-Born-Feodorov constitutive laws Maxwell equations in chiral media were deduced. Full time-dependent problems will be reduced to the consideration of Weyl operators.
- Numerical Mathematics
- Theoretical Mathematics