Ultraviolet–Infrared Mixing on the Noncommutative Minkowski Space in the Yang–Feldman Formalism

Zahn, Jochen

doi:10.1007/s00023-011-0153-9

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Moreover, there is no analogue of the Osterwalder-Schrader theorem allowing a smooth transition between the Euclidean and the Minkowskian regimes, and a Minkowskian version of the Grosse-Wulkenhaar model is affected by strange divergencies [34]. On the other hand, ultraviolet-infrared mixing effects, albeit different from the ones in the Euclidean setting, have also been pointed out in QFT on Minkowskian noncommutative spacetime defined through the Hamiltonian approach [2] and through the Yang-Feldman equation [35]. Further discussion of the adiabatic limit of QFT on QST, in the Yang-Feldman approach, can be found in [16,33].…”

Section: Introductionmentioning

confidence: 99%

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

Doplicher,

Morsella,

Pinamonti

2019

Preprint

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The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which seems difficult to remove. We solve this problem here by another strategy: the fields at a point in the interaction Lagrangian are replaced by the fields at a quantum point , described by an optimally localized state on QST; the resulting Lagrangian density agrees with the previous one after spacetime integration, but gives rise to a different interaction hamiltonian. But now the methods of perturbative Algebraic Quantum Field Theory can be applied, and produce an ultraviolet finite perturbation expansion of the interacting observables. If the obtained theory is tested in an equilibrium state at finite temperature the adiabatic cutoff in time becomes immaterial, namely it has no effect on the correlation function at any order in perturbation theory. Moreover, the interacting vacuum state can be obtained in the vanishing temperature limit. It is nevertheless important to stress that the use of states which are optimally localized for a given observer brakes Lorentz invariance at the very beginning.

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Section: Introductionmentioning

confidence: 99%

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

Doplicher,

Morsella,

Pinamonti

2019

Preprint

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Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

Doplicher

Morsella

Pinamonti

2020

Commun. Math. Phys.

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On the renormalization of non-commutative field theories

et al. 2013

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This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for noncommutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.1 It is possible to remedy this problem by considering supersymmetry, e.g. the Wess-Zumino model on Moyal space [5]. However, in the present paper we restrict our attention to non-supersymmetric models.2 In this context, we should mention the so-called twisted approach to φ 4 -theory for which there has been some recent progress (see for instance reference [8]), but which we will not discuss here.3 In the Grosse-Wulkenhaar case, the initial proof was established by its authors by using the Wilson-Polchinski renormalization group approach in a matrix base. A later proof [10] relied on multi-scale analysis.

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Ultraviolet–Infrared Mixing on the Noncommutative Minkowski Space in the Yang–Feldman Formalism

Cited by 3 publications

References 23 publications

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

On the renormalization of non-commutative field theories

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