Standard Model Of Quantum Physics In Clifford Algebra, The

Claude Daviau, Jacques Bertrand

• Publisher: WSPC
• Year: 2015
• Topic: Biological Sciences
• eBook ISBN:
  9789814719889
• Subtopic: Science General
• Index: Biological Sciences

We extend to gravitation our previous study of a quantum wave for all particles and antiparticles of each generation (electron + neutrino + u and d quarks for instance). This wave equation is form invariant under Cl 3 *, then relativistic invariant. It is gauge invariant under the gauge group of the standard model, with a mass term: this was impossible before, and the consequence was an impossibility to link gauge interactions and gravitation.

We extend to gravitation our previous study of a quantum wave for all particles and antiparticles of each generation (electron + neutrino + u and d quarks for instance). This wave equation is form invariant under Cl 3 *, then relativistic invariant. It is gauge invariant under the gauge group of the standard model, with a mass term: this was impossible before, and the consequence was an impossibility to link gauge interactions and gravitation.

Readership: Graduate students and professionals in particle physics or mathematical physics.
Key Features:

• Presents an argument that gravitation is compatible with quantum physics
• The gauge group of the standard model is obtained from the geometry of space-time
• Magnetic monopoles are joined to this new frame

Chapter 1

Clifford algebras

This chapter presents what a Clifford algebra is, then we study the algebra of an Euclidean plane and the algebra of 3-dimensional physical space which is also the algebra of the Pauli matrices. We put the space-time and the relativistic invariance there. Then we present the space-time algebra and the Dirac matrices. We finally present the Clifford algebra of a 6-dimensional space-time, needed by the electro-weak and strong interactions.

It is quite usual in a physics book to put the mathematics into appendices even if they are necessary to understand the main part of the book. As it is impossible to understand the part containing physics without the Clifford algebras, we make here again a complete presentation¹ of this necessary tool. Why is this mathematical tool necessary? The physics of light and quantum physics use waves, therefore they use trigonometric functions, then also the exponential function, then necessarily products. The addition of vectors is not enough, a multiplication must be used. Then we must consider two operations, addition and multiplication of vectors. The mathematical tool of Clifford algebra is ready to be used in this case.

We shall only speak here about Clifford algebras on the real field. Algebras on the complex field also exist and we could expect complex algebras to be key point for quantum physics. The main algebra used here is also an algebra on the complex field, but it is its structure of real algebra² which is useful.

Our aim is not to say everything about any Clifford algebra but simply to give to our lecturer tools to understand the next chapters of this book.

Another very interesting introduction to the subject is the book by D...

Table of contents

• Cover
• Halfitle
• Title
• Copyright
• Foreword
• Contents
• Introduction
• 1. Clifford algebras
• 2. Dirac equation
• 3. The homogeneous nonlinear wave equation
• 4. Invariance of electromagnetic laws
• 5. Miscellaneous
• 6. Electro-weak interactions: The lepton case
• 7. Electro-weak and strong interactions
• 8. Magnetic monopoles
• 9. Inertia and gravitation
• 10. Conclusion
• Appendix A Calculations in Clifford algebras
• Appendix B Electron+neutrino+quarks
• Appendix C The hydrogen atom
• Bibliography
• Index