Clifford algebras and some special problems in physics

Today, the many different algebraic systems are used for expressing of the laws and concepts of physics. One of the them is Clifford algebras. In this thesis, after defining general of Clifford algebra, the general properties of Clifford algebras which are defined in different space are given. Cl2 Clifford algebras are the similar to the quaternion algebra. Cl3 and Cl4 Clifford algebras are the similar to the complexified quaternion algebra. These similarities are also shown. Hyperbolic octonion algebra which have the similar properties with basis of Clifford algebras but not associated is also defined. Clifford algebras are used in many field of physics. But in this thesis using by Clifford algebras, the some special applications in the mathematical physics, analytic dynamics, special relativity, electromagnetic theory and quantum mechanic have been indicated. Finally, Proca field and Proca Maxwell equations are reduced to one equation by hyperbolic octonions. Keyword: Clifford Algebras, Quaternion Algebra, Hyperbolic Octonion Algebra, Electrodynamics, Relativistic Mechanics