The exceptional Jordan eigenvalue problem

被引：23
作者：
Dray, T [1 ]
Manogue, CA
机构：
[1] Oregon State Univ, Dept Math, Corvallis, OR 97331 USA
[2] Oregon State Univ, Dept Phys, Corvallis, OR 97331 USA
来源：
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 1999年 / 38卷 / 11期
关键词：
Field Theory; Elementary Particle; Quantum Field Theory; Quantum Mechanic; Eigenvalue Problem;
D O I：
10.1023/A:1026699830361
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We discuss the eigenvalue problem for 3 x 3 octonionic Hermitian matrices which is relevant to the Jordan formulation of quantum mechanics. In contrast to the eigenvalue problems considered in our previous work, all eigenvalues are real and solve the usual characteristic equation. We give an elementary construction of the corresponding eigenmatrices, and we further Speculate on a possible application to particle physics.
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收藏
页码：2901 / 2916
页数：16
相关论文
共 14 条
[1]   On a certain algebra of quantum mechanics [J].
Albert, AA .
ANNALS OF MATHEMATICS, 1934, 35 :65-73
[2]   THE EXCEPTIONAL SIMPLE LIE ALGEBRA-F4 AND ALGEBRA-E6 [J].
CHEVALLEY, C ;
SCHAFER, RD .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1950, 36 (02) :137-141
[3]   Finding octonionic eigenvectors using Mathematica [J].
Dray, T ;
Manogue, CA .
COMPUTER PHYSICS COMMUNICATIONS, 1998, 115 (2-3) :536-547
[4]  
Dray T., 1998, Adv. Appl. Clifford Algebr, V8, P341, DOI [10.1007/BF03043104, DOI 10.1007/BF03043104]
[5]  
Freudenthal H., 1964, ADV MATH, V1, P145
[6]  
FREUDENTHAL H, 1953, P KON NED AKAD WET A, V56, P195
[7]   On an algebraic generalization of the quantum mechanical formalism [J].
Jordan, P ;
Von Neumann, J ;
Wigner, E .
ANNALS OF MATHEMATICS, 1934, 35 :29-64
[8]   The multiplication of quantum mechanical quantities. [J].
Jordan, P. .
ZEITSCHRIFT FUR PHYSIK, 1933, 80 (5-6) :285-291
[9]   FINITE LORENTZ TRANSFORMATIONS, AUTOMORPHISMS, AND DIVISION-ALGEBRAS [J].
MANOGUE, CA ;
SCHRAY, J .
JOURNAL OF MATHEMATICAL PHYSICS, 1993, 34 (08) :3746-3767
[10]   THE CHARACTERISTIC EQUATION FOR 3 X 3 MATRICES OVER OCTAVES [J].
OGIEVETSKII, OV .
RUSSIAN MATHEMATICAL SURVEYS, 1981, 36 (02) :189-190
12