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Self-energies on deformed spacetimes
High Energy Physics - Theory · Submitted 5 Jun 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus for a specific point (0,3) in the parameter-space (kappa_f,kappa_g), a covariant theta-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object.
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The abstract, sentence by sentence
We study one-loop photon (Pi) and neutrino (Sigma) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetric-constant tensor theta^{mu nu}. For the general fermion-photon (S_f) and photon self-interaction (S_g) the closed form results reveal self-energies besetting with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(mu^2(theta p)^2). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon self-energy in four-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of theta^{mu nu} and setting deformation parameters (kappa_f,kappa_g)=(0,3). In this case the neutrino two-point function vanishes. Thus for a specific point (0,3) in the parameter-space (kappa_f,kappa_g), a covariant theta-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. While in two-dimensional space the photon self-energy is finite for arbitrary (kappa_f,kappa_g) combinations, the neutrino self-energy still contains an superficial IR divergence.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study one-loop photon (Pi) and neutrino (Sigma) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetric-constant tensor theta^{mu nu}. | contribution 0.98 | 0.91 | 0.04 | asserted 0.97 |
| s1 | For the general fermion-photon (S_f) and photon self-interaction (S_g) the closed form results reveal self-energies besetting with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(mu^2(theta p)^2). | result 1.00 | 0.89 | 0.08 | asserted 1.00 |
| s2 | In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. | result 1.00 | 0.86 | 0.05 | asserted 1.00 |
| s3 | We show that the photon self-energy in four-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of theta^{mu nu} and setting deformation parameters (kappa_f,kappa_g)=(0,3). | result 0.96 | 0.93 | 0.26 | asserted 0.99 |
| s4 | In this case the neutrino two-point function vanishes. | result 1.00 | 0.84 | 0.06 | asserted 1.00 |
| s5 | Thus for a specific point (0,3) in the parameter-space (kappa_f,kappa_g), a covariant theta-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. | interpretation 0.59 | 0.92 | 0.81 | asserted 0.96 |
| s6 | While in two-dimensional space the photon self-energy is finite for arbitrary (kappa_f,kappa_g) combinations, the neutrino self-energy still contains an superficial IR divergence. | result 0.96 | 0.87 | 0.05 | asserted 1.00 |
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The paper
Original abstract
We study one-loop photon (Pi) and neutrino (Sigma) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetric-constant tensor theta^{mu nu}. For the general fermion-photon (S_f) and photon self-interaction (S_g) the closed form results reveal self-energies besetting with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(mu^2(theta p)^2). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon self-energy in four-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of theta^{mu nu} and setting deformation parameters (kappa_f,kappa_g)=(0,3). In this case the neutrino two-point function vanishes. Thus for a specific point (0,3) in the parameter-space (kappa_f,kappa_g), a covariant theta-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. While in two-dimensional space the photon self-energy is finite for arbitrary (kappa_f,kappa_g) combinations, the neutrino self-energy still contains an superficial IR divergence.
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How the literature uses it
12 arXiv papers cite this in 44 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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Thus for a specific point $(0,3)$ in the parameter-space $(\kappa_f,\kappa_g)$, a covariant $\theta$-exact approach is able to produce a divergence-free result for the one-loop quantum corrections, having also both well-defined commutative limit and point-like limit of an extended object.
Papers citing it · 35 sentences without a confident label
Uses its method or tool 1 paper
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For coupling of photons to the right-handed neutrinos we use a state-of-the-art version of gauge field theory (GFT) deformed by the spacetime noncommutativity (NC) [ref] employed in our previous work [ref] .
Inferring type and scale of noncommutativity from the PTOLEMY experiment · Introduction · 0.98
Compares with it 1 paper
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Tensor structure remain exactly the same as for the photon-bubble-diagram in Fig 2 from [ref] , as one would expect.
Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution · Four-photon-tadpole contributions in the limit $D→4-ϵ$ · 0.94
Cites it as background 4 papers
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In the focus of [ref] was a gauge field theoretical model incorporating spacetime noncommutativity (NC), which had been previously shaped next to the mature phase, so to ultimately display a trouble-free UV/IR behavior at the quantum level, both without and with supersymmetry [ref] .
Inferring type and scale of noncommutativity from the PTOLEMY experiment · Introduction · 0.87
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First we note that, since the Feynman rules of the 3- and 4-photon self-couplings ([ref]), are already given in previous papers [ref] and [ref] , respectively, we shall not repeat them here.
Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of quadratic noncommutative IR divergences · The action · 0.80
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Much of efforts went in taming divergences related to the ultraviolet-infrared connection/mixing, see for example [ref] .
Two-Point Functions on Deformed Spacetime · Discussion and conclusion · 0.94
What it cites · 26 sentences without a confident label
Builds on 2 papers
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Considering neutrino self-energy ([ref]), our results extends the prior works [ref] by completing the behavior for general $κ_f$.
On UV/IR mixing in noncommutative gauge field theories · Discussion · 1.00
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Considering neutrino self-energy ([ref]), our results extends the prior works [ref] by completing the behavior for general $κ_f$.
Neutrino propagation in noncommutative spacetimes · Discussion · 1.00
Uses the method or tool of 1 paper
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Employing the parametrization given in Appendix A and [ref] , we are enabled to follow the general procedure of dimensional regularization in computing one-loop two point functions.
Yukawa couplings and seesaw neutrino masses in noncommutative gauge theory · Computing photon two-point function using dimensional regularization · 0.98
Compares with 3 papers
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Due to the dominance of the photon-loop contributions the overall sign for the 2d photon self-energy is changed and for some values of $κ_f=κ_g$ its contribution gets enhanced by a large factor with respect to the previous result [ref] .
Noncommutative Two-Dimensional Gauge Theories · Conclusion · 0.98
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After a lengthy computation we obtained the following compact form of the photon-loop contribution to the photon two-point function in D-dimensions, [equation] Clearly the above structure is much more reacher with respect to earlier $θ$-exact without SW map results [ref] .
Perturbative analysis on infrared aspects of noncommutative QED on R^4 · Computing photon two-point function using dimensional regularization · 0.99
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One-loop contributions as a function of $κ_f$ receive the same Lorentz structure as in [ref] .
Neutrino propagation in noncommutative spacetimes · One-loop neutrino self-energy · 0.99
Cites as background 17 papers
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Next follows theoretical studies of one loop quantum properties [ref] , as well as studies of some new physical phenomena, like breaking of Landau-Yang theorem, [ref] , etc.
Seiberg Witten Map and the Axial Anomaly in Noncommutative Field Theory · Introduction · 0.96
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Next follows theoretical studies of one loop quantum properties [ref] , as well as studies of some new physical phenomena, like breaking of Landau-Yang theorem, [ref] , etc.
Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map · Introduction · 0.96
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Next follows theoretical studies of one loop quantum properties [ref] , as well as studies of some new physical phenomena, like breaking of Landau-Yang theorem, [ref] , etc.
The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics · Introduction · 0.96
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