# What Kind of a Beast Is It? The exceptional Lie Algebra e8 and the Standard Model of Particle Physics

# What Kind of a Beast Is It? The exceptional Lie Algebra e8 and the Standard Model of Particle Physics

**Abstract: **The standard model of particle physics does an excellent job of using the Lie algebra su(3) x su(2)_{L} x u(1) to describe the internal symmetries that are seen in particle physics experiments. But this Lie algebra is messy and ad hoc. Since the theories of electromagnetism u(1) and the weak force su(2)_{L} were first unified, decades ago, theoreticians have dreamed of finding a more elegant theory that includes the strong force (grand unified theories—called GUTS) and possibly supersymmetry and gravity.

In this talk, I will describe my own decades of such attempts, together with many collaborators (beginning with my postdoctoral advisor David Fairlie and most recently with Tevian Dray and Robert Wilson) to find such a unified theory using the exceptional Lie algebras e_{6} and e_{8}. These theories are most beautifully described using extensions of the complex numbers called quaternions and octonions and their “split” cousins. This somewhat biographical story will highlight how a dedication to understanding the nature of complicated mathematical objects (What kind of a beast is it?) and a commitment to following where the mathematics leads is finally paying off.

In spite of all the scary, technical words in this abstract, I will only assume that you know about spin and complex numbers at the level of PH 425 (Quantum Fundamentals) and Lorentz Transformations at the level of PH 335 (Theoretical Mechanics). All the other mathematical elements are generalizations of these. If you want a chance to play with some of the new mathematical structures, I’ll be giving a workshop in the Phys Bits Seminar on Wednesday, 1/31 at 4 pm.**Speaker bio: **please see https://osuper.science.oregonstate.edu/people/corinne-manogue