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this is my first thread at Physics-forums. I am currently working on GUT's and try to learn

the Higgs mechanism. Therefore my supervisor gave me a toy model. This model is a SU(4) gauge theory with a infinite series of 4+ \bar 4 as Matter fields (fermions) and a Higgs sector which consist of a singlet and a 15.

I tried to break the symmetry down to a SU(3)xU(1) by inserting VEV into the lagrangian and to minimize the higgs potential. Group theory tolds me that the representations decompose as

[tex] 15 = 8 + 3 +\bar 3 +1 [/tex]

[tex]4 = 3 +1 [/tex]

[tex]\bar 4 = \bar 3+ 1 [/tex]

I choose a vev which forces the 8 and the 1 of the 15 to be heavy. These are

[tex] <8>_{SU(3)} = l 1_{3x3} , <1>_{SU(3)} = -3 l => <15>_{SU(4)} = l ~diag(1,1,1,-3)[/tex]

as well as

[tex] <1>_{SU(4)}= w~ diag(1,1,1,1) [/tex]

The Result I got for the minima of the potential is that

l = 0 and w < 0.

I Think my Higgspotential is wrong. It is of the Form

[tex]Tr[(w_1 1_R /4 + w_2 15_R /3 + v~1_{4x4}/(\mu 4))^4 ][/tex]

Here 1_R and 15_R are the Representations of the SU(4) Higgs sector and the rest are constants.

I hope you could help me or enjoined the reading.

Thank you for reading

timb00