• DOI:10.1103/PhysRevD.65.084044
• Corpus ID: 16104623

Coproduct and star product in field theories on Lie-algebra noncommutative space-times

@article{AmelinoCamelia2001CoproductAS,
  title={Coproduct and star product in field theories on Lie-algebra noncommutative space-times},
  author={Giovanni Amelino-Camelia and Michele Arzano},
  journal={Physical Review D},
  year={2001},
  volume={65},
  pages={084044}
}

• G. Amelino-Camelia, M. Arzano
• Published 13 May 2001
• Mathematics
• Physical Review D

We propose a new approach to field theory on $\kappa$-Minkowski non-commutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical non-commutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the $\kappa$-Poincare' coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in $\kappa$-Minkowski the coproduct and the star product must indeed treat momenta in a non-symmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in $\kappa$-Minkowski field theories it is convenient to introduce the concepts of "planar" and "non-planar" Feynman loop-diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical non-commutative space-times.