# Exceptional Groups and Physics

@article{Ramond2003ExceptionalGA, title={Exceptional Groups and Physics}, author={Pierre Ramond}, journal={arXiv: High Energy Physics - Theory}, year={2003} }

Quarks and leptons charges and interactions are derived from gauge theories associated with symmetries. Their space-time labels come from representations of the non-compact algebra of Special Relativity. Common to these descriptions are the Lie groups stemming from their invariances. Does Nature use Exceptional Groups, the most distinctive among them? We examine the case for and against their use. They do indeed appear in charge space, as the Standard Model fits naturally inside the exceptional…

## 21 Citations

The Extended Relativity Theory in Clifford Spaces

- Physics
- 2004

An introduction to some of the most important features of the Extended Relativity theory in Clifford-spaces (C-spaces) is presented whose "point" coordinates are non-commuting Clifford-valued…

On the Large N Limit of Exceptional Jordan Matrix Models, Chern-Simons Foliations and M, F Theory

- Mathematics
- 2007

The large N → ∞ limit of the Exceptional F4, E6 Jordan Matrix Models of Smolin-Ohwashi leads to a novel Chern-Simons Membrane Lagrangian which is the suitable candidate Lagrangian for…

On the noncommutative and nonassociative geometry of octonionic space time, modified dispersion relations and grand unification

- Mathematics
- 2007

The octonionic geometry (gravity) developed long ago by Oliveira and Marques, J. Math. Phys. 26, 3131 (1985) is extended to noncommutative and nonassociative space time coordinates associated with…

On the masses of elementary particles

- Physics
- 2011

We make an attempt to describe the spectrum of masses of elementary particles, as it comes out empirically in six distinct scales. We argue for some rather well defined mass scales, like the electron…

Exceptional super Yang-Mills in 27 + 3 and worldvolume M-theory

- Mathematics
- 2020

Non-associative Gauge Theory

- Mathematics
- 2005

We present a construction of gauge theory which its structure group is not a Lie group, but a Moufang loop which is essentially non-associative. As an example of non-associative algebra, we take…

Basic twist quantization of the exceptional Lie algebra g2

- Mathematics
- 2005

We present the formulas for twist quantization of g2, corresponding to the solution of a classical YB equation with support in the eight-dimensional Borel subalgebra of g2. The considered chain of…

Geometry of exceptional super Yang-Mills theories

- MathematicsPhysical Review D
- 2019

Some time ago, Sezgin, Bars and Nishino have proposed super Yang-Mills theories (SYM's) in $D=11+3$ and beyond. Using the "Magic Star" projection of $\mathfrak{e}_{8(-24)}$, we show that the…

Exceptional Lie algebras, SU(3) and Jordan pairs: part 2. Zorn-type representations

- Mathematics
- 2014

A representation of the exceptional Lie algebras reflecting a simple unifying view, based on realizations in terms of Zorn-type matrices, is presented. The role of the underlying Jordan pair and…

Magic Coset Decompositions

- Mathematics
- 2012

By exploiting a \mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special Kahler symmetric rank-3 coset E7( 25)= E6(…

## References

Algebraic Dreams

- Art
- 2001

Nature's attraction to unique mathematical structures provides powerful hints for unraveling her mysteries. None is at present as intriguing as eleven-dimensional M-theory. The search for exceptional…