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

References in corpus (7)

• Noncommutative Gravity
• Lorentz Conserving Noncommutative Standard Model
• Tensor Operators in Noncommutative Quantum Mechanics
• Unusual High-Energy Phenomenology of Lorentz-Invariant Noncommutative Field Theories
• Dynamical symmetries in noncommutative theories
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Quantum Field Theory on Quantum Spacetime

Cited by in corpus (1)

• Tensor Coordinates in Noncommutative Mechanics