### Abstract

A special quaternion representation is constructed for a pair of relativistic vectors and skew-symmetric tensors on the basis of the group theory of Lorentz transformations. The construction has considerable advantages over the conventional vector-tensor description. It is pointed out that pairs of Minkowski vectors as well as certain scalars and skew-symmetric tensors can also be interpreted as simple components of more complex physical quantities, each of them expressed by a single quaternion. As an example a concise relativistic quaternion formulation of Maxwell's electrodynamics is presented. The relativistic covariance can be maintained even for the existence of magnetic monopoles.

Original language | English |
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Article number | 013 |

Pages (from-to) | 3245-3254 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 24 |

Issue number | 14 |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*24*(14), 3245-3254. [013]. https://doi.org/10.1088/0305-4470/24/14/013

**A quaternion representation of the Lorentz group for classical physical applications.** / Abonyi, I.; Bito, J. F.; Tar, J.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 24, no. 14, 013, pp. 3245-3254. https://doi.org/10.1088/0305-4470/24/14/013

}

TY - JOUR

T1 - A quaternion representation of the Lorentz group for classical physical applications

AU - Abonyi, I.

AU - Bito, J. F.

AU - Tar, J.

PY - 1991

Y1 - 1991

N2 - A special quaternion representation is constructed for a pair of relativistic vectors and skew-symmetric tensors on the basis of the group theory of Lorentz transformations. The construction has considerable advantages over the conventional vector-tensor description. It is pointed out that pairs of Minkowski vectors as well as certain scalars and skew-symmetric tensors can also be interpreted as simple components of more complex physical quantities, each of them expressed by a single quaternion. As an example a concise relativistic quaternion formulation of Maxwell's electrodynamics is presented. The relativistic covariance can be maintained even for the existence of magnetic monopoles.

AB - A special quaternion representation is constructed for a pair of relativistic vectors and skew-symmetric tensors on the basis of the group theory of Lorentz transformations. The construction has considerable advantages over the conventional vector-tensor description. It is pointed out that pairs of Minkowski vectors as well as certain scalars and skew-symmetric tensors can also be interpreted as simple components of more complex physical quantities, each of them expressed by a single quaternion. As an example a concise relativistic quaternion formulation of Maxwell's electrodynamics is presented. The relativistic covariance can be maintained even for the existence of magnetic monopoles.

UR - http://www.scopus.com/inward/record.url?scp=0039022829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039022829&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/24/14/013

DO - 10.1088/0305-4470/24/14/013

M3 - Article

AN - SCOPUS:0039022829

VL - 24

SP - 3245

EP - 3254

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 14

M1 - 013

ER -