## F4 and E8: Wrong Assumption: E8 Cannot Unify Fermions and Bosons. Useful Truth: F4 and E8 Lie Algebras Have Both Commutator and Anticommutator Structure.

**Authors:** Frank Dodd Tony Smith Jr

Realistic Physics models must describe both commutator Bosons and anticommutator Fermions so that spin and statistics are consistent. The usual commutator structure of Lie Algebras can only describe Bosons, so a common objection to Physics models that describe both Bosons and Fermions in terms of a single unifiying Lie Algebra (for example, Garrett Lisi's E8 TOE) is that they violate consistency of spin and statistics by using Lie Algebra commutators to describe Fermions. However, Pierre Ramond has shown in hep-th/0112261 as shown that the exceptional Lie Algebra F4 can be described using anticommutators as well as commutators. This essay uses the periodicity property of Real ticommutators as well as commutators so that it may be possible to construct a realistic Physics model that uses the exceptional LiClifford Algebras to show that E8 can also be described using ane Algebra E8 to describe both Bosons and Fermions. E8 also inherits from F4 Triality-based symmetries between Bosons and Fermions that can give the useful results of SuperSymmetry without requiring conventional SuperPartner particles that are unobserved by LHC.

**Comments:** 6 Pages.

**Download:** **PDF**

### Submission history

[v1] 2012-08-18 14:34:01

**Unique-IP document downloads:** 209 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*