ABSTRACT
The standard 16-dimensional and new 64-dimensional representations of the Clifford algebras in the terms of Dirac matrices are under consideration. The matrix 64-dimensional representation of the Clifford algebra over the field of real numbers is presented. The relationship of this representation to the matrix representation of 28-dimensional algebra, which contains the standard and additional spin operators, is given. The role of matrix representations of the Clifford algebra in the quantum field theory is described. The role of matrix representations of and algebras in the proof of Fermion-Boson duality property of the Dirac and higher spin Dirac-like equations is demonstrated.
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