FIZIKA B 10 (2001)  4, 187-210

 size 215 kBsize 605 kB



Institute Ruđer Bošković, HR-10000 Zagreb, Croatia
E-mail address:

Dedicated to Professor Kseno Ilakovac on the occasion of his 70th birthday

Received 7 January 2002; Accepted 18 February 2002
Online 6 April 2002

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.

PACS numbers: 02.10.Jf, 03.65.-w
UDC 530.145

Keywords: quaternion, octonion, division algebra, quantion, quantum, unification

Copyright by The Croatian Physical Society
For problems or questions please contact