Dirac \(\gamma\)-equation, classical gauge fields and Clifford algebra (Q1276109)

The Dirac equation for spin 1/2 particles can be obtained by formally factorizing the Klein-Gordon operator. The author presents another factorization of the Klein-Gordon operator thus arriving at what he calls the Dirac \(\gamma\) equation. For the latter he considered the following questions: decomposition into the even and odd parts; plane wave solutions; gauge groups; conservation laws; canonical forms of the Dirac \(\gamma\) equation. The Yang-Mills and Maxwell \(\gamma\) equations are considered also. Finally, a system of equations named Dirac-Yang-Mills system of \(\gamma\) equations is introduced which describes Dirac's field interacting with the Yang-Mills gauge field.