2. Standard Model
The Standard Model is known as a gauge theory, and is based on the symmetry group SU(3)C⊗SU(2)L⊗U(1)Y; as described in the previous section the symmetry group of standard model, describes the strong, weak and electromagnetic interactions, via the exchange of 8 massless gluons and 1 massless photon, respectively, for the strong and electromagnetic interactions, and three massive bosons, W± and Z, for the weak interaction2. Leptons and quarks which are the building blocks of the fermionic matter, are characterized in the structure below, (3)
(4)
(5)
and each quark appears in its three different colours, as shown below2,
(6)
The notation in the above equations is also illustrated in the table below.
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Given these conditions, theory will involve Quantum Electrodynamics with a massless photon, a charged scalar field ϕ and mass μ4.
However, if μ2 > 0, the field will obtain a vacuum expectation value as below,
(17)
and in such a case the global U(1) symmetry will be spontaneously broken.
A parameterized ϕ has the following form,
(18)
where h and χ are the Higgs boson and the Goldstone boson, respectively, and represent real scalar fields with no vacuum expectation values. If we substitute this scalar field into the original Lagrangian, we obtain the following4,
(19)
This new derived Lagrangian describes a photon of mass mA = ev, a Higgs boson h with the following mass,
(20)
along with a massless Goldstone χ. In addition, to remove the χ-Aμ mixing can be removed from the Lagrangian through the following gauge
Witkin, H. A., Moore, C. A., Goodenough, D. R., & Cox, P. W. (1977). Field-dependent and
Hewitt, Paul G. Conceptual Physics 10th Edition. 10th ed. San Francisco: Pearson Addison Wesley, 2006.
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Even though their co-incidence on this point is not explicit but one can infer an implicit similar pattern in their theories
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1 David Halliday, Robert Resnick, and Jearl Walker, Fundamentals of Physics, Extended, 5th ed. (NewYork:Wiley, 1997) 361
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Recker, D. M. (2011, March 3). Utah State University. Retrieved from Utah State University web site: http://inst.usu.edu/~mimi/courses/6260/theorists/Ausubel/aususc.html