IVF3. A Broken Symmetry Standard Model Vacuum.

We can modify Eq. (IVF2-4) to obtain broken symmetry vacuums.  For example, if we want a broken SU(6) vacuum, , that is invariant under , we can put an m label on the f’s and suppose

(IVF3-1)         

We can then break the SU(2) and one U(1) symmetry by the replacement

(IVF3-2)        

with a, b, and  being constants, to obtain the vacuum .  This gives a partially broken symmetry similar to that used in the standard model. 

Interaction Properties for the Broken Symmetry SU(6) Vacuum.

If we assume the characteristics of the interactions are correlated with the symmetry properties of the vacuum , then the strong interactions would correspond to the invariant SU(3) and the electroweak  interactions to the invariant U(1), and the broken SU(2).  In that case, the basic spin ½ states have the following interaction characteristics:

● States 1, 2, and 3 are quarklike (from the  invariance group) except that they have no weak interaction.

● State 4 is neutrinolike (weak charge + ½ ).

● State 5 is electronlike (weak charge – ½ ) with an electromagnetic charge (from the U(1) invariance group)  times that of states 1, 2, and 3.

● And state 6 has no strong, electromagnetic or (standard) weak interactions. 

These characteristics imply that the (scalar) SU(2) symmetry breaking terms  have the same electroweak transformation properties as the conjectured symmetry breaking, mass-inducing scalar boson field of the standard model.¹ 

Notes:

1. Weinberg, S., The Quantum Theory of Fields, Vol. II, pg. 309. (Cambridge Univ. Press, Cambridge, 1996).