2024/12/03 by García, J. Antonio, Cruz-Alvarez, Rafael
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2412.02633
A relation between the Dirac bracket (DB) and Nambu bracket (NB) is presented. The Nambu bracket can be related with Dirac bracket if we can write the DB as a generalized Poisson structure. The NB associated with DB have all the standard properties of the original DB. When the dimension of the phase space is s+2 where s is the number of second class constraints, the associated Nambu structure has s+2 entries and reduces to the Dirac bracket when s of its entries are fixed to be the second class constraints. In general, when the dimension of phase space is d=r+s a new Nambu structure that describes correctly the constrained dynamics can also be constructed but in thsi case addicional conditidionts are requiered. In that case the associated NB corresponds to a ``Dirac-Nambu'' bracket with r entries.