Original scientific paper
Inherently relativistic quantum theory. Part III. Quantionic algebra
Emile Grgin
; Institute Ruđer Bošković, HR-10000 Zagreb, Croatia
Abstract
Quantum mechanics and relativity are not compatible at the structural level, and this makes it very difficult to unify them. The incompatibility might mean that a complete quantum theory unified with relativity exists, but is unknown, while standard quantum mechanics, as a special case, cannot be relativistic. If so, searching for generalizations is well justified, but the question is how. An old idea is to substitute a structurally richer algebra for the field of complex numbers, but such attempts have not brought the theory closer to relativity in the past. The present work is also based on this idea, but, unlike previous attempts, is not searching for new number systems among existing mathematical structures. From general considerations developed in the first two parts of this work, a new mathematical structure, referred to as the quantionic algebra, is derived as a theorem in the present paper. It is unique, manifestly relativistic, and generalizes the field of complex numbers in a manner consistent with quantum theory.
Keywords
quaternion; octonion; division algebra; quantion; quantum; unification
Hrčak ID:
304052
URI
Publication date:
1.10.2001.
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