 
FIZIKA B 10 (2001) 4, 187210
INHERENTLY RELATIVISTIC QUANTUM THEORY
PART III. QUANTIONIC ALGEBRA
EMILE GRGIN
Institute Ruđer Bošković, HR10000 Zagreb, Croatia
Email address: eg137@ix.netcom.com
Dedicated to Professor Kseno Ilakovac on the occasion of his 70^{th}
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
