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Clifford Algebras and Possible Kinematics
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Clifford Algebras and Possible Kinematics
Інший ID:
2000 Mathematics Subject Classification: 11E88; 15A66; 53A17
Посилання:
Clifford Algebras and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 28 назв. — англ.
Підтримка:
I wish to thank the referees for their careful reading of this paper and their suggestions for
valuable improvements.
Дата:
2007
Переглядів:
434
Завантажень:
258
Анотація:
We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. In addition we give conformal models for these spacetimes.
