Fermions and noncommutative theories

Abstract

By using a framework where the object of noncommutativity ${\theta }^{\mu \nu }$ represents independent degrees of freedom, we study the symmetry properties of an extended $x+\theta$ space-time, given by the group $P$', which has the Poincaré group $P$ as a subgroup. In this process we use the minimal canonical extension of the Doplicher, Fredenhagen and Roberts algebra. It is also proposed a generalized Dirac equation, where the fermionic field depends not only on the ordinary coordinates but on ${\theta }^{\mu \nu }$ as well. The dynamical symmetry content of such fermionic theory is discussed, and we show that its action is invariant under $\mathcal{P}$'.

10 pages, Latex, published version

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Cited by in corpus (15)

• Noncommutative relativistic particles
• Quantum complex scalar fields and noncommutativity
• Tensor Coordinates in Noncommutative Mechanics
• Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• 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
• Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
• Noncommutativity and Duality through the Symplectic Embedding Formalism
• The Strong Interaction Model in DFR noncommutative space-time
• From Noncommutative Sphere to Nonrelativistic Spin
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
• The standard electroweak model in the noncommutative $DFR$ space-time