A Novel View on the Physical Origin of E8
| dc.creator | Pavsic, Matej | |
| dc.date | 2008-06-26 | |
| dc.date.accessioned | 2026-07-07T11:33:56Z | |
| dc.date.available | 2026-07-07T11:33:56Z | |
| dc.description | We consider a straightforward extension of the 4-dimensional spacetime $M_4$ to the space of extended events associated with strings/branes, corresponding to points, lines, areas, 3-volumes, and 4-volumes in $M_4$. All those objects can be elegantly represented by the Clifford numbers $X\equiv x^A γ_A \equiv x^{a_1 ...a_r} γ_{a_1 ...a_r}, r=0,1,2,3,4$. This leads to the concept of the so-called Clifford space ${\cal C}$, a 16-dimensional manifold whose tangent space at every point is the Clifford algebra ${\cal C \ell }(1,3)$. The latter space besides an algebra is also a vector space whose elements can be rotated into each other in two ways: (i) either by the action of the rotation matrices of SO(8,8) on the components $x^A$ or (ii) by the left and right action of the Clifford numbers $R=$exp$ [α^A \gam_A]$ and $S=$exp$ [β^A \gam_A]$ on $X$. In the latter case, one does not recover all possible rotations of the group SO(8,8). This discrepancy between the transformations (i) and (ii) suggests that one should replace the tangent space ${\cal C \ell}(1,3)$ with a vector space $V_{8,8}$ whose basis elements are generators of the Clifford algebra ${\cal C \ell}(8,8)$, which contains the Lie algebra of the exceptional group E$_8$ as a subspace. E$_8$ thus arises from the fact that, just as in the spacetime $M_4$ there are $r$-volumes generated by the tangent vectors of the spacetime, there are $R$-volumes, $R=0,1,2,3,...,16$, in the Clifford space ${\cal C}$, generated by the tangent vectors of ${\cal C}$. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0806.4365 | |
| dc.identifier | http://arxiv.org/abs/0806.4365 | |
| dc.identifier | J.Phys.A41:332001,2008 | |
| dc.identifier | doi:10.1088/1751-8113/41/33/332001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/198075 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | A Novel View on the Physical Origin of E8 | |
| dc.type | text |