A Wave Equation including Leptons and Quarks for the Standard Model of Quantum Physics in Clifford Algebra

Claude Daviau^*, Jacques Bertrand

Le Moulin de la Lande, Pouillé-les-Coteaux, France.

DOI: 10.4236/jmp.2014.518210                

Abstract

A wave equation with mass term is studied for all fermionic particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks u and d with three states of color and antiquarks and . This wave equation is form invariant under the group generalizing the relativistic invariance. It is gauge invariant under the U(1)×SU(2)×SU(3) group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra Cl_1,5. Then many features of the standard model, charge conjugation, color, left waves, and Lagrangian formalism, are obtained in the frame of the first quantization.

Keywords

Invariance Group, Dirac Equation, Electromagnetism, Weak Interactions, Strong Interactions, Clifford Algebras

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Daviau, C. and Bertrand, J. (2014) New Insights in the Standard Model of Quantum Physics in Clifford Algebra. JePublie, Pouille-les-Coteaux. http://hal.archives-ouvertes.fr/hal-00907848
[2]	Daviau, C. and Bertrand, J. (2014) Journal of Modern Physics, 5, 1001-1022. http://dx.doi.org/10.4236/jmp.2014.511102
[3]	Daviau, C. (1993) Equation de Dirac non lineaire. Ph.D. Thesis, Universite de Nantes, Nantes.
[4]	Daviau, C. (1997) Advances in Applied Clifford Algebras, 7, 175-194.
[5]	Daviau, C. (2005) Annales de la Fondation Louis de Broglie, 30, 409-428.
[6]	Daviau, C. (2011) L’espace-temps double. JePublie, Pouille-les-coteaux.
[7]	Daviau, C. (2012) Advances in Applied Clifford Algebras, 22, 611-623. http://dx.doi.org/10.1007/s00006-012-0351-7
[8]	Daviau, C. (2012) Double Space-Time and More. JePublie, Pouille-les-Coteaux.
[9]	Daviau, C. (2012) Nonlinear Dirac Equation, Magnetic Monopoles and Double Space-Time. CISP, Cambridge.
[10]	Deheuvels, R. (1993) Tenseurs et spineurs. PUF, Paris.
[11]	Hestenes, D. (1986) A Unified Language for Mathematics and Physics and Clifford Algebra and the Interpretation of Quantum Mechanics. In: Chisholm, J.S.R. and Common, A.K., Eds., Clifford Algebras and Their Applications in Mathematics and Physics, Reidel, Dordrecht, 1-23.
[12]	Weinberg, S. (1967) Physical Review Letters, 19, 1264-1266. http://dx.doi.org/10.1103/PhysRevLett.19.1264
[13]	Daviau, C. (2014) Gauge Group of the Standard Model in Cl1,5. ICCA10, Tartu. http://hal.archives-ouvertes.fr/hal-01055145
[14]	de Broglie, L. (1924) Annales de la Fondation Louis de Broglie, 17.