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

By Giovanni Amelino-Camelia, Michele Arzano. 2001

171 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/169234dee047bdc2501cf922e2ee1cafeebc89c7

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Citations in the corpus

Quantum-Spacetime Phenomenology (2008, background): “For other (non-canonical) noncommutative spacetimes we are still struggling in the search for a satisfactory formulation of a quantum field theory [335, 64], and it is at this point legitimate to worry that such a formulation of dynamics in those spacetimes does not exist.”
Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory (2015, background): “[63–67] and [68, 69] for gauge theories in particular.”