Hyperbolic Quaternion Formulation of Electromagnetism

被引：45
作者：
Demir, Suleyman [1 ]
Tanisli, Murat [1 ]
Candemir, Nuray [1 ]
机构：
[1] Anadolu Univ, Dept Phys, TR-26470 Eskisehir, Turkey
来源：
ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2010年 / 20卷 / 3-4期
关键词：
Hyperbolic quaternion; electromagnetism; magnetic monopole; MAXWELL EQUATIONS; ELECTRON THEORY; DIRAC; CLIFFORD; ALGEBRA; ELECTRODYNAMICS; REFORMULATION; HYPERNUMBERS; OCTONIONS; GEOMETRY;
D O I：
10.1007/s00006-010-0209-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, after presenting the hyperbolic quaternion formalism, an alternative representational method is proposed for the formulation of classical and generalized electromagnetism in the case of the existence of magnetic monopoles and massive photons. Maxwell's equations and relevant field equations are derived in compact, simpler and elegant forms. These equations are compared with their vectorial, complex quaternionic, dual quaternionic and octonionic representations.
引用
收藏
页码：547 / 563
页数：17
相关论文
共 71 条
[31]   Comment on formulating and generalizing Dirac's, Proca's, and Maxwell's equations with biquaternions or Clifford numbers [J].
Gsponer, A ;
Hurni, JP .
FOUNDATIONS OF PHYSICS LETTERS, 2001, 14 (01) :77-85
[32]  
Hamilton W., 1899, ELEMENTS QUATERNIONS
[33]  
Hestenes D., 1966, SPACE TIME ALGEBRA
[34]  
HESTENES D, 1991, ADV APPL CLIFFORD AL, V1, P51
[35]   NEW FORMULATION OF CLASSICAL ELECTRODYNAMICS [J].
IMAEDA, K .
NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-GENERAL PHYSICS RELATIVITY ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS, 1976, 32 (01) :138-162
[36]  
Kassandrov V.V., 1995, Gravit. Cosmol, V1, P216
[37]  
KELLNER M, 1994, J JEWISH THOUGHT PH, V4, P1
[38]   Hypernumbers and relativity [J].
Koplinger, Jens .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) :954-969
[39]   Gravity and electromagnetism on conic sedenions [J].
Koplinger, Jens .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) :948-953
[40]   Signature of gravity in conic sedenions [J].
Koplinger, Jens .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) :942-947
12345678