TY - JOUR
AU - Girard, Patrick R.
AB - The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism, and general relativity. ; This book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions. ; The use of Cli?ord algebra in mathematical physics and engineering has grown rapidly in recent years. Cli?ord had shown in 1878 the equivalence of two - proaches to Cli?ord algebras: a geometrical one based on the work of Grassmann and an algebraic one using tensor products of quaternion algebras H. Recent - velopmentshave favoredthe geometric approach(geometric algebra) leading to an algebra (space-time algebra) complexi?ed by the algebra H? H presented below and thus distinct from it. The book proposes to use the algebraic approach and to de?ne the Cli?ord algebra intrinsically, independently of any particular matrix representation, as a tensor product of quaternion algebras or as a subalgebra of such a product. The quaternion group thus appears as a fundamental structure of physics. One of the main objectives of the book is to provide a pedagogical introd- tion to this new calculus, starting from the quaternion group, with applications to physics.The volume is intended for professors,researchersand students in physics and engineering, interested in the use of this new quaternionic Cli?ord calculus. The book presents the main concepts in the domain of, in particular, the quaternion algebra H, complex quaternions H(C), the Cli?ord algebra H? H real and complex, the multivector calculus and the symmetry groups: SO(3), the Lorentz group, the unitary group SU(4) and the symplectic unitary group USp(2,H). Among the applications in physics, we examine in particular, special relativity, classical electromagnetism and general relativity.; Quaternions.- Rotation groups SO(4) and SO(3).- Complex quaternions.- Clifford algebra.- Symmetry groups.- Special relativity.- Classical electromagnetism.- General relativity.- Conclusion.; The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have priviledged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity. The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus. ; First book presenting Clifford algebras in an algebraic way in terms of a tensor product of quaternion algebras with applications to relativistic physics The quaternion group consequently appears as a fundamental structure of physics ; The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism, and general relativity. The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus.
TI - Quaternions, algèbre de Clifford et physique relativiste
DA - 2007-06-25
UR - https://www.deepdyve.com/lp/springer-e-books/quaternions-alg-bre-de-clifford-et-physique-relativiste-shb8p5Rom4
DP - DeepDyve
ER -