Signal propagation on κ -Minkowski spacetime and nonlocal two-point functions

Abstract

We study the propagation of quantum fields on κ-Minkowsi spacetime. Starting from the noncommutative partition function for a free field written in momentum space we derive the Feynman propagator and analyze the non-trivial singularity structure determined by the group manifold geometry of momentum space. The additional contributions due to such singularity structure result in a deformed field propagation which can be alternatively described in terms of an ordinary field propagation determined by a source with a blurred spacetime profile. We show that the κ-deformed Feynman propagator can be written in terms of vacuum expectation values of a commutative nonlocal quantum field. For sub-Planckian modes the κ-deformed propagator corresponds to the vacuum expectation value of the time-ordered product of non-local field operators while for trans-Plankian modes this is replaced by the Hadamard two-point function, the vacuum expectation value of the anti-commutator of non-local field operators. * Electronic address: michele.arzano@roma1.infn.it † Electronic address: consoli.

$κ$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory

“…Another interesting issue is the relation of our construction with the approaches based on star products [33][34][35][36][38][39][40]42,[44][45][46]. In particular, [41] focuses on the lightlike κ-Minkowski spacetime, and, despite being based on a star-product approach whose fundamental ontology is that of commutative functions, it derives some results that are in line with ours so far: the free scalar QFT is undeformed, and a dependence on κ seems to be confined to the interacting theory.…”

“…There is, however, no current agreement in the literature on the correct formulation of noncommutative Quantum Field Theory (QFT), although there is a sizeable literature on the subject [33][34][35][36][37][38][39][40][41]. Recently, there has been a resurgence in interest for QFT κ-Minkowski [41][42][43][44][45][46][47][48], and perhaps the most important difference between approaches regards the basic ontology. Most approaches are based on a commutative algebra of functions, over which a non-local "star" product, involving an infinite number of derivatives of the fields, is defined.…”

$κ$-deformed complex scalar field: conserved charges, symmetries and their impact on physical observables

“…Starting with the time translations, we first need to define the variation of the field components δ T 0 a p , δ T 0 b p , where by δ T 0 we denote the translation generated by an infinitesimal parameter ǫ µ = (ǫ, 0). We know translations act on the Fourier components as phase transformations a p → e iǫω p a p ≈ a p + iǫω p a p (30) and therefore…”

Quantum scalar field theories with fractional operators

“…• A non-local kinetic term K = ( − m 2 ) E 2 * − can arise for a scalar field in κ-Minkowski non-commutative spacetime [116]. The propagator and its branch cuts were studied in [117].…”