A natural star product for 4-d κ-Minkowski space is used to investigate various classes of κ-Poincaré invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual ϕ 4 theory. κ-Poincaré invariance forces the integral involved in the actions to be a twisted trace, thus defining a Kubo-Martin-Schwinger (KMS) weight for the noncommutative (C Ã -)algebra modeling the κ-Minkowski space. In all the field theories, the twist generates different planar one-loop contributions to the 2-point function which are at most UV linearly diverging. Some of these theories are free of UV/IR mixing. In the others, UV/IR mixing shows up in non-planar contributions to the 2-point function at exceptional zero external momenta while staying finite at nonzero external momenta. These results are discussed together with the possibility for the KMS weight relative to the quantum space algebra to trigger the appearance of KMS state on the algebra of observables.
We study the limits to the localizability of events and reference frames in the κ-Minkowski quantum spacetime. Our main tool will be a representation of the κ-Minkowski commutation relations between coordinates, and the operator and measurement theory borrowed from ordinary quantum mechanics. Spacetime coordinates are described by operators on a Hilbert space, and a complete set of commuting observables cannot contain the radial coordinate and time at the same time. The transformation between the complete sets turns out to be the Mellin transform, which allows us to discuss the localizability properties of states both in space and time. We then discuss the transformation rules between inertial observers, which are described by the quantum κ-Poincaré group. These too are subject to limitations in the localizability of states, which impose further restrictions on the ability of an observer to localize events defined in a different observer's reference
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