Avoidance of a Landau pole by flat contributions in QED

Klaczynski, Lutz; Kreimer, Dirk

doi:10.1016/J.AOP.2014.02.019

Title: Avoidance of a Landau pole by flat contributions in QED

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Abstract

We consider massless Quantum Electrodynamics in the momentum scheme and carry forward an approach based on Dyson–Schwinger equations to approximate both the β-function and the renormalized photon self-energy (Yeats, 2011). Starting from the Callan–Symanzik equation, we derive a renormalization group (RG) recursion identity which implies a non-linear ODE for the anomalous dimension and extract a sufficient but not necessary criterion for the existence of a Landau pole. This criterion implies a necessary condition for QED to have no such pole. Solving the differential equation exactly for a toy model case, we integrate the corresponding RG equation for the running coupling and find that even though the β-function entails a Landau pole it exhibits a flat contribution capable of decreasing its growth, in other cases possibly to the extent that such a pole is avoided altogether. Finally, by applying the recursion identity, we compute the photon propagator and investigate the effect of flat contributions on both spacelike and timelike photons. -- Highlights: •We present an approach to approximate both the β-function and the photon self-energy. •We find a sufficient criterion for the self-energy to entail the existence of a Landau pole. •We study non-perturbative ‘flat’ contributions that emerge within the contextmore »« less

Authors:

Klaczynski, Lutz ^[1]; Kreimer, Dirk ^[2]

Department of Physics, Humboldt University Berlin, 12489 Berlin (Germany)
Alexander von Humboldt Chair in Mathematical Physics, Humboldt University, Berlin 12489 (Germany)

Publication Date:: Thu May 15 00:00:00 EDT 2014

OSTI Identifier:: 22314810

Resource Type:: Journal Article

Journal Name:: Annals of Physics (New York)

Additional Journal Information:: Journal Volume: 344; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANOMALOUS DIMENSION; APPROXIMATIONS; COUPLING; DIFFERENTIAL EQUATIONS; NONLINEAR PROBLEMS; PHOTONS; PROPAGATOR; QUANTUM ELECTRODYNAMICS; RENORMALIZATION; SCHWINGER FUNCTIONAL EQUATIONS; SELF-ENERGY

Citation Formats


                    Klaczynski, Lutz, and Kreimer, Dirk. Avoidance of a Landau pole by flat contributions in QED.  United States: N. p., 2014. 
        Web.  doi:10.1016/J.AOP.2014.02.019.

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                    Klaczynski, Lutz, & Kreimer, Dirk. Avoidance of a Landau pole by flat contributions in QED.  United States.  https://doi.org/10.1016/J.AOP.2014.02.019

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                    Klaczynski, Lutz, and Kreimer, Dirk. 2014.  
        "Avoidance of a Landau pole by flat contributions in QED".  United States.  https://doi.org/10.1016/J.AOP.2014.02.019.

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@article{osti_22314810,

  title        = {Avoidance of a Landau pole by flat contributions in QED},

  author       = {Klaczynski, Lutz and Kreimer, Dirk},

  abstractNote = {We consider massless Quantum Electrodynamics in the momentum scheme and carry forward an approach based on Dyson–Schwinger equations to approximate both the β-function and the renormalized photon self-energy (Yeats, 2011). Starting from the Callan–Symanzik equation, we derive a renormalization group (RG) recursion identity which implies a non-linear ODE for the anomalous dimension and extract a sufficient but not necessary criterion for the existence of a Landau pole. This criterion implies a necessary condition for QED to have no such pole. Solving the differential equation exactly for a toy model case, we integrate the corresponding RG equation for the running coupling and find that even though the β-function entails a Landau pole it exhibits a flat contribution capable of decreasing its growth, in other cases possibly to the extent that such a pole is avoided altogether. Finally, by applying the recursion identity, we compute the photon propagator and investigate the effect of flat contributions on both spacelike and timelike photons. -- Highlights: •We present an approach to approximate both the β-function and the photon self-energy. •We find a sufficient criterion for the self-energy to entail the existence of a Landau pole. •We study non-perturbative ‘flat’ contributions that emerge within the context of our approach. •We discuss a toy model and how it is affected by flat contributions.},

  doi          = {10.1016/J.AOP.2014.02.019},

  url          = {https://www.osti.gov/biblio/22314810},
  journal      = {Annals of Physics (New York)},

  issn         = {0003-4916},

  number       = Complete,

  volume       = 344,

  place        = {United States},

  year         = {Thu May 15 00:00:00 EDT 2014},

  month        = {Thu May 15 00:00:00 EDT 2014}

}

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