LXXVI. <i>Quaternionic form of relativity</i>

Silberstein, Ludwik

doi:10.1080/14786440508637276

Cited by 68 publications

(53 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Eq. (3.15) is equivalent to the old quaternion form of Maxwell's equations [64]. Furthermore, with vector like elements, the hyperbolic quaternions should give easier and more successful generalization of the classical electromagnetism than the other non-associative algebras such as octonions.…”

Section: Hyperbolic Quaternions and Classical Electromagnetismmentioning

confidence: 99%

Hyperbolic Quaternion Formulation of Electromagnetism

Demi̇r

Tanışlı

Candemir

2010

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

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. Mathematics Subject Classification (2000). 00A79, 8A25, 17D99.

show abstract

Section: Hyperbolic Quaternions and Classical Electromagnetismmentioning

confidence: 99%

Hyperbolic Quaternion Formulation of Electromagnetism

Demi̇r

Tanışlı

Candemir

2010

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

show abstract

“…The conventional Maxwell's equations (7) follow the first choice of four-potential which describe the electromagnetic fields given by (8) and thus, violates the duality invariance due to presence of source current. Here, we have discussed the alternative choice of second four-potential which produces the electric and magnetic fields given by equations (10) to satisfy the another kind of Maxwell's equations given by equations (11) and (12). These Maxwell's equations (11) or (12) are visualized as dual Maxwell's equations as they may be obtained from the usual Maxwell's equations (7) under duality transformations (2,3,4).…”

Section: Discussionmentioning

confidence: 99%

“…Starting with the concept of invariance of the electromagnetic duality in source free Maxwell's equations (1), we have shown that the Maxwell's equations (1) remain invariant under duality transformations (2,3,4) with the choice of four potential either to express the electromagnetic fields given by (8) or by (10). The conventional Maxwell's equations (7) follow the first choice of four-potential which describe the electromagnetic fields given by (8) and thus, violates the duality invariance due to presence of source current.…”

Section: Discussionmentioning

confidence: 99%

“…A comprehensive list of references has already been published in quaternion bibliographies [5] on the practical applications of quaternion analysis on various applied topics in theoretical and mathematical physics. The quaternionic formulation of electrodynamics has a long history [6][7][8][9][10][11][12][13][14][15][16], stretching back to Maxwell himself [6][7][8] who used real (Hamilton) quaternion in his original manuscript 'on the application of quaternion to electromagnetism' and in his celebrated book "Treatise on Electricity and Magnetism". However, Maxwell [6][7][8] used quaternion as the substitute of common vector calculus which made his field equations difficult for his contemporaries [17,18] because the quaternionic formulation in three-space brings several complications as the field of applicability of real quaternions is Euclidean four-space [19][20][21][22][23].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Revisiting Quaternion Dual Electrodynamics

Bisht

Negi

2008

Int J Theor Phys

View full text Add to dashboard Cite

“…APS can also be viewed as the 4-dimensional algebra of complex paravectors [15]. It is also isomorphic to complex quaternions, which have along history of applications in relativity, [16,17] The formulation of relativity in STA can be characterized as absolute, in that physical paths, fields, and other properties of objects are expressed independent of any observer.…”

Section: Introductionmentioning

confidence: 99%

Relativity in Clifford's Geometric Algebras of Space and Spacetime

Baylis

Sobczyk

2004

International Journal of Theoretical Physics

View full text Add to dashboard Cite

Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships between formulations of special relativity in the spacetime algebra (STA) Cℓ 1,3 of the underlying Minkowski vector space, and in the algebra of physical space (APS) Cℓ 3 . STA lends itself to an absolute formulation of relativity, in which paths, fields, and other physical properties have observer-independent representations. Descriptions in APS are related by a one-to-one mapping of elements from APS to the even subalgebra STA + of STA. With this mapping, reversion in APS corresponds to hermitian conjugation in STA. The elements of STA + are all that is needed to calculate physically measurable quantities (called measurables) because only they entail the observer dependence inherent in any physical measurement. As a consequence, every relativistic physical process that can be modeled in STA also has a representation in APS, and vice versa. In the presence of two or more inertial observers, two versions of APS present themselves. In the absolute version, both the mapping to STA + and hermitian conjugation are observer dependent, and the proper basis vectors of any observer are persistent vectors that sweep out timelike planes in spacetime. To compare measurements by different inertial observers in APS, we express them in the proper algebraic basis of a single observer. This leads to the relative version of APS, which can be related to STA by assigning every inertial observer in STA to a single absolute frame in STA. The equivalence of inertial observers makes this permissible. The mapping and hermitian conjugation are then the same for all observers. Relative APS gives a covariant representation of relativistic physics with spacetime multivectors represented by multiparavectors in APS. We relate the two versions of APS as consistent models within the same algebra.

show abstract

LXXVI. Quaternionic form of relativity

Cited by 68 publications

References 0 publications

Hyperbolic Quaternion Formulation of Electromagnetism

Hyperbolic Quaternion Formulation of Electromagnetism

Revisiting Quaternion Dual Electrodynamics

Relativity in Clifford's Geometric Algebras of Space and Spacetime

Contact Info

Product

Resources

About