Some aspects of the homogeneous formalism in field theory and gauge invariance

Marcella Palese; Ekkehart Winterroth

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Using the Clifford bundle formalism we show that Frenet equations of classical differential geometry or its spinor version are the appropriate equations of motion for a classical spinning particle. We show that particular values of the curvatures appearing in Darboux bivector of the spinor form of Frenet equations produce a "classical" Dirac-Hestenes equation. Using the concept of multivector Lagrangians and Hamiltonians we provide a Lagrangian and Hamiltonian approach for our theory...

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Systems of rays in the presence of distribution of hyperplanes

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Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems $v_{H}$ on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields $v_{H}$ are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical...