Dynamical symmetries in noncommutative theories

Abstract

In the present work we study dynamical space-time symmetries in noncommutative relativistic theories by using the minimal canonical extension of the Doplicher, Fredenhagen and Roberts algebra. Our formalism is constructed in an extended space-time with independent degrees of freedom associated with the object of noncommutativity ${\theta }^{\mu \nu }$. In this framework we consider theories that are invariant under the Poincaré group $\mathcal{P}$ or under its extension ${\mathcal{P}}^{\prime }$, when translations in the extra dimensions are permitted. The Noether's formalism adapted to such extended $x+\theta$ space-time is employed.

20 pages, Latex. Some changes in the text. Version accepted for publication in Physical Review D

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• Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime
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• Noncommutative Particles in Curved Spaces
• Some aspects of quantum mechanics and field theory in a Lorentz invariant noncommutative space
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Maximal acceleration in a Lorentz invariant non-commutative space-time
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• Quantum Gravity models - brief conceptual summary