Abstract
We construct a new model for relativistic particle on the noncommutative plane, using the symplectic formalism of constrained systems. We suggest a shortcut approach to construct the gauged Lagrangian, using the Poisson algebra of constraints, without calculating the whole procedure of symplectic formalism. We also propose an approach for the systems, in which the symplectic formalism is not applicable, due to the truncation of production of secondary constraints at the first level. After gauging the model, we obtain the corresponding generators of gauge transformations of the physical system. Finally, by extracting the Poisson structure of all constraints, we show the effect of gauging on the canonical structure of the phase spaces of both primary and gauged models.
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Notes
In the context of noncommutative theories, e is added into the action as the einbein variable in order to exclude the massless cases.
As we mentioned in our short cut method in this article usually two correction terms containing WZ variable are added the gauged Lagrangian.
Although correction terms in BFT method can be truncated in some cases, or make a closed form in some others, but it is hard to handle and is a time consuming procedure.
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Monemzadeh, M., Dehghani, M. & Nejad, S.A. Gauging the Relativistic Particle Model on the Noncommutative Plane. Int J Theor Phys 56, 1793–1806 (2017). https://doi.org/10.1007/s10773-017-3326-6
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DOI: https://doi.org/10.1007/s10773-017-3326-6