Clifford Algebra, its generalisation and their applications to symmetries and relativistic wave equations

Abstract

This thesis work essentially relates to the study of the EigenVector and EigenValue structure of the matrices of the generalised clifford algebra and their possible interpretation in elementary particle physics. Sigma - operation, a generalisation of Dirac's procedure to obtain 4x4 matrices, in his famous electron wave equation forms the basic idea of initiation to this research problem. If a linear combination of higher dimensional matrices is considered, then its EigenVectors turn out to be degenerative; The concept of holicity matrices is introduced to resolve this degeneracy. The energy and holicity belong to a hierarchy of Eigenvalues. In this thesis these concepts are extended and related to the Clifford algebra of anticommuting matrices to the case of the generalised Clifford Algebra of matrices, the nth roots of the unit matrix, satisfying a generalised commutation rule. Then they are applied to the study of Symmetry principles and Elementary Particle Physics.