Translational Invariance and Noncommutative Field Theories

Abstract

Implications of noncommutative field theories with commutator of the coordinates of the form $[x^{\mu },x^{\nu }]=i{\Lambda }_{\omega }^{\mu \nu }{x}^{\omega }$with nilpotent structure constants are investigated. It is shown that a free quantum field theory is not affected by noncommutativity, but that invariance under translations is broken and hence the energy-momentum conservation is not respected. The new energy-momentum law is expressed by a Poincaré-invariant equation and the resulting kinematics is developed and applied to the astrophysical puzzle related with the observed violation of the GZK cutoff.

arXiv comment10 pages; Invited talk at the Qauntum Gravity Phenomenology section of the Tenth Marcel Grossmann Meeting on General Relativity, Rio de Janeiro, Brazil, 20-26 July, 2003