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- W2078373386 abstract "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 ) ∩ Sp ( 2 , 4 ) transformations. We find that the general solution to the classical equations of motion has no linear term in the evolution parameter, τ, 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 τ derivative that is covariant under local Sp ( 2 ) transformations between the phase space variables x μ ( τ ) and p μ ( τ ) . 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." @default.
- W2078373386 created "2016-06-24" @default.
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- W2078373386 date "2009-10-01" @default.
- W2078373386 modified "2023-10-14" @default.
- W2078373386 title "Beyond the relativistic point particle: A reciprocally invariant system and its generalisation" @default.
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- W2078373386 doi "https://doi.org/10.1016/j.physletb.2009.09.020" @default.
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