Special bracket versus Jacobi bracket on the classical phase space of general relativistic test particle

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Authors

JANYŠKA Josef

Year of publication 2014
Type Article in Periodical
Magazine / Source International Journal of Geometrical Methods in Modern Physics
MU Faculty or unit

Faculty of Science

Citation
Web http://www.worldscientific.com/doi/abs/10.1142/S0219887814600202
Doi http://dx.doi.org/10.1142/S0219887814600202
Field General mathematics
Keywords Spacetime; phase space; dynamical connection; dynamical 2-form; dynamical 2-vector; almost-cosymplectic–contact structure; almost-coPoisson–Jacobi structure; contact structure; Jacobi structure; special phase function; special bracket
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Description The classical phase space of general relativistic classical test particle (here called, for short, "phase space") is defined as the first jet space of motions regarded as timelike one-dimensional submanifolds of spacetime. By the projectability assumption, we define the subsheaf of special phase functions with a special Lie bracket and we compare the Lie algebra of special phase functions with the structures obtained on the phase space by the standard Hamiltonian approach.
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