Unitarity of time-like noncommutative gauge theories: the violation of Ward identities in time-ordered perturbation theory

Ohl, Thorsten; Rückl, R.; Zeiner, Jörg

doi:10.1016/j.nuclphysb.2003.10.022

Cited by 31 publications

(27 citation statements)

References 10 publications

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“…One could then impose the standard dispersion relations as a new renormalization condition. At the one-loop level the only remaining effect of the noncommutativity would then be the 16 Possibly, one could also have a linear dependence on k 2 in order to allow for a field strength renormalization.…”

Section: Resultsmentioning

confidence: 99%

“…In any case δ ′ is nilpotent at tree level, and thus the Ward identity will be satisfied at tree level in any quantization scheme that respects the classical equations of motion, as the Yang-Feldman formalism. In Appendix B, we explicitly show this for Compton scattering at second order, a process which is known to violate the Ward identity at tree level in the Hamiltonian approach to NCQED [16].…”

Section: Setupmentioning

confidence: 91%

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Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism

Zahn

2010

Phys. Rev. D

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We study quantum electrodynamics on the noncommutative Minkowski space in the Yang-Feldman formalism. Local observables are defined by using covariant coordinates. We compute the two-point function of the interacting field strength to second order and find the infrared divergent terms already known from computations using the so-called modified Feynman rules. It is shown that these lead to nonlocal renormalization ambiguities. Also new nonlocal divergences stemming from the covariant coordinates are found. Furthermore, we study the supersymmetric extension of the model. For this, the supersymmetric generalization of the covariant coordinates is introduced. We find that the nonlocal divergences cancel. At the one-loop level, the only effect of noncommutativity is then a momentum-depenent field strength normalization. We interpret it as an acausal effect and show that its range is independent of the noncommutativity scale.1 Strictly speaking, one should replace Θ µν in (1.1) by a central operator Q µν whose joint spectrum is Σ. But for the present purposes, it suffices to consider a fixed Θ ∈ Σ, as long as one keeps in mind that it transforms as a tensor under Lorentz transformations.2 Here, we do not consider the theories obtained by adding a Grosse-Wulkenhaar potential [5]. As shown in [6], their Minkowski space version is badly divergent. We also do not consider the so-called 1/p 2 theories [7], and the models inspired by the twist approach of Wess and coworkers [8].3 In general, planarity is defined by the genus of the Riemann surface onto which the graph may be drawn [10].

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Section: Resultsmentioning

confidence: 99%

Section: Setupmentioning

confidence: 91%

Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism

Zahn

2010

Phys. Rev. D

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“…In [18] the time-ordered perturbation theory (TOPT) was introduced for theories with noncommutative time, concluding that the construction leads to a unitary theory. In [24] it was shown that the noncommutative QED thus constructed does not satisfy Ward identities, therefore this procedure for recovering unitarity is not consistent either.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative time in quantum field theory

Salminen¹,

Tureanu²

2011

Phys. Rev. D

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We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-Källén equation) and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate.The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of light-like noncommutativity.

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“…which for x 0 = t and x ′0 = t ′ (being the case when Θ 0µ = 0) reduces to (2.72). This approach seems promising in some respects, meaning that one may extend the formalism to non-commutative gauge fields, although (among many others) the question of unitarity is still unclear [198].…”

Section: Time-ordered Perturbation Theorymentioning

confidence: 99%

Gauge Theories on Deformed Spaces

Blaschke

Kronberger

Sedmik³

et al. 2010

SIGMA

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Abstract. The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold-Moyal spaces and renormalizability, but we will also review other deformations and try to point out common features. This review will by no means be complete and cover all approaches, it rather reflects a highly biased selection.

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Unitarity of time-like noncommutative gauge theories: the violation of Ward identities in time-ordered perturbation theory

Cited by 31 publications

References 10 publications

Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism

Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism

Noncommutative time in quantum field theory

Gauge Theories on Deformed Spaces

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