Grand Unified Theories
John Iliopoulos · 2024
One of the most remarkable achievements of modern theoretical physics has been the construction of the standard model for weak, electromagnetic and strong interactions. It is a gauge theory based on the group U (1) ⊗ SU (2) ⊗ SU (3) which is spontaneously broken to U (1) ⊗ SU (3). This relatively simple model epitomizes our present knowledge of elementary Particle interactions. The model contains three types of fields: The gauge fields. There are twelve spin-one boson fields which can be classified into the (1,8) ⊗ (3,1) ⊗ (1,1) representation of SU (2) ⊗ SU ( 3 ). The first eight are the gluons which mediate strong interactions between quarks and the last four are ( W + , W − , Z 0 and γ), the vector bosons of the electroweak theory. Fermion matter fidds. The basic unit is the ‘family’ consisting of fifteen two-component complex spinor fields which, under SU (2)⊗ SU (3), form the representation (2,1)⊗ (1,1)⊗(2,3) ⊗ (1,3) ⊗ (1,3). The prototype is the electron family https://www.w3.org/1998/Math/MathML" display="block"> ν e e - L ; e R ; u i d i L ; u i R ; d i R ( 2,1 ) ( 1,1 ) ( 2,3 ) ( 1,3 ) ( 1,3 ) i = 1,2 , 3 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003575924/18a74078-c2b9-45b1-8f31-1a452039284e/content/eq1263.tif "/>