The Georgi-Glashow Model

The Georgi-Glashow model is a grand unified theory that unifies the Standard Model gauge group into SU(5).

This file currently contains informal-results about the Georgi-Glashow group.

def GeorgiGlashow.GaugeGroupI : InformalDefinition

The gauge group of the Georgi-Glashow model, i.e., SU(5).

Equations

• GeorgiGlashow.GaugeGroupI = { deps := [] }

def GeorgiGlashow.inclSM : InformalDefinition

The homomorphism of the Standard Model gauge group into the Georgi-Glashow gauge group, i.e., the group homomorphism SU(3) × SU(2) × U(1) → SU(5) taking (h, g, α) to blockdiag (α ^ 3 g, α ^ (-2) h).

See page 34 of https://math.ucr.edu/home/baez/guts.pdf

Equations

• GeorgiGlashow.inclSM = { deps := [`GeorgiGlashow.GaugeGroupI, `StandardModel.GaugeGroupI] }

def GeorgiGlashow.inclSM_ker : InformalLemma

The kernel of the map inclSM is equal to the subgroup StandardModel.gaugeGroupℤ₆SubGroup.

See page 34 of https://math.ucr.edu/home/baez/guts.pdf

Equations

• GeorgiGlashow.inclSM_ker = { deps := [`GeorgiGlashow.inclSM, `StandardModel.gaugeGroupℤ₆SubGroup] }

def GeorgiGlashow.embedSMℤ₆ : InformalDefinition

The group embedding from StandardModel.GaugeGroupℤ₆ to GaugeGroupI induced by inclSM by quotienting by the kernel inclSM_ker.

Equations

• GeorgiGlashow.embedSMℤ₆ = { deps := [`GeorgiGlashow.inclSM, `StandardModel.GaugeGroupℤ₆, `GeorgiGlashow.GaugeGroupI, `GeorgiGlashow.inclSM_ker] }