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The standard model of quantum physics in Clifford algebra. (English) Zbl 1335.81009

Hackensack, NJ: World Scientific (ISBN 978-981-4719-86-5/hbk; 978-981-4740-29-6/ebook). xii, 227 p. (2016).
This book presents the standard model of quantum physics in Clifford algebra. Chapter 1 presents what Clifford algebra is. The algebra of a Euclidean plane and the algebra of 3-dimensional physical space are studied. After putting the space-time and the relativistic invariance, the algebra of Dirac matrices is discussed. Clifford algebra of a 6-dimensional space-time needed by the electro-weak and strong interaction is described. The link between the invariant form of Dirac equation and the Lagrangian density is presented in Chapter 2. The question of negative energies is studied in Chapter 3. It is proved that with the wave equation presented, all usual plane waves have a positive energy. The relativistic invariance is studied which introduces a greater invariance group and a second-space-time manifold. The charge conjugation is discussed and it is shown how the non-linear wave equation gets the quantification and the true results in the case of H atom. The invariance of electromagnetic laws is covered in Chapter 4. Chapter 5 describes the first consequence of the two space-time manifolds and the dilations between these two manifolds. Chapter 6 covers electro-weak interactions with reference to leptons while Chapter 7 is on electro-weak interactions with reference to quark sector. Recent experimental works on magnetic monopoles are presented in Chapter 8. Chapter 9 is on inertia and gravitation while in Chapter 10 concluding remarks are given.

MSC:

81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81V22 Unified quantum theories
15A66 Clifford algebras, spinors
81V10 Electromagnetic interaction; quantum electrodynamics
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
00A79 Physics
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