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

Abstract

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.

LaTex, 16 pages. Some remarks on the differences between planar and nonplanar diagrams have been added

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• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Quantum theory's last challenge

Cited by in corpus (130)

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• New realizations of Lie algebra kappa-deformed Euclidean space
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• The Search for Quantum Gravity Signals
• Improved limit on quantum-spacetime modifications of Lorentz symmetry from observations of gamma-ray blazars
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• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
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• Generalized Weyl systems and kappa-Minkowski space
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• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• Lorentz invariant field theory on kappa-Minkowski space
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
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• Noncommutative Differential Forms on the kappa-deformed Space
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