Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8194483 | Physics Letters B | 2009 | 7 Pages |
Abstract
We investigate a reciprocally invariant system proposed by Low and Govaerts et al., whose action contains both the orthogonal and the symplectic forms and is invariant under global O(2,4)â©Sp(2,4) transformations. We find that the general solution to the classical equations of motion has no linear term in the evolution parameter, Ï, but only the oscillatory terms, and therefore cannot represent a particle propagating in spacetime. As a remedy, we consider a generalisation of the action by adopting a procedure similar to that of Bars et al., who introduced the concept of a Ï derivative that is covariant under local Sp(2) transformations between the phase space variables xμ(Ï) and pμ(Ï). This system, in particular, is similar to a rigid particle whose action contains the extrinsic curvature of the world line, which turns out to be helical in spacetime. Another possible generalisation is the introduction of a symplectic potential proposed by Montesinos. We show how the latter approach is related to Kaluza-Klein theories and to the concept of Clifford space, a manifold whose tangent space at any point is Clifford algebra Cl(8), a promising framework for the unification of particles and forces.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Nuclear and High Energy Physics
Authors
Matej PavÅ¡iÄ,