Relativistic wave equations and multiple Dirac algebras
Mitchell, Horace Glover
Guertin, Ralph F.
Master of Arts
A new formalism for finding and studying relativistic wave equations has been developed. Using the algebra of matrices for the Dirac equation, higher order algebras/ called multiple Dirac algebras, were created and a proof was given that the matrices for any such equation were essentially elements of these algebras. Further / the transformation properties of the elements of the algebras under the proper Lorentz group were determined in order to specify the elements a^u The classical analysis of this problem, due to Bhaba, was reproduced and compared to the analysis in the new formalism. The use of the multiple Dirac algebras in determining the algebraic structure of the matrices was demonstrated in a series of examples and followed by a discussion of problems that could be approached with the formalism.