Advertisement

Renormalization of the QED of self-interacting second order spin \( \frac{1}{2} \) fermions.

  • Carlos A. Vaquera-Araujo
  • Mauro Napsuciale
  • René Ángeles-Martınez
Article

Abstract

We study the one-loop level renormalization of the electrodynamics of spin 1/2 fermions in the Poincaré projector formalism, in arbitrary covariant gauge and including fermion self-interactions, which are dimension four operators in this framework. We show that the model is renormalizable for arbitrary values of the tree level gyromagnetic factor g within the validity region of the perturbative expansion, αg2 ≪ 1. In the absence of tree level fermion self-interactions, we recover the pure QED of second order fermions, which is renormalizable only for g = ±2. Turning off the electromagnetic interaction we obtain a renormalizable Nambu-Jona-Lasinio-like model with second order fermions in four space-time dimensions.

Keywords

Electromagnetic Processes and Properties Renormalization Regularization and Renormalons Gauge Symmetry 

References

  1. [1]
    R.P. Feynman, An Operator calculus having applications in quantum electrodynamics, Phys. Rev. 84 (1951) 108 [INSPIRE].
  2. [2]
    V. Fock, Proper time in classical and quantum mechanics, Phys. Z. Sowjetunion 12 (1937) 404 [INSPIRE].Google Scholar
  3. [3]
    R. Feynman and M. Gell-Mann, Theory of Fermi interaction, Phys. Rev. 109 (1958) 193 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  4. [4]
    C. Schubert, Perturbative quantum field theory in the string inspired formalism, Phys. Rept. 355 (2001) 73 [hep-th/0101036] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  5. [5]
    L. Biedenharn, M. Han and H. Van Dam, Two-component alternative to Diracs equation, Phys. Rev. D 6 (1972) 500 [INSPIRE].ADSGoogle Scholar
  6. [6]
    N. Cufaro Petroni, P. Gueret, J. Vigier and A. Kyprianidis, Second order wave equation for spin 1/2 fields, Phys. Rev. D 31 (1985) 3157 [INSPIRE].MathSciNetADSGoogle Scholar
  7. [7]
    N. Cufaro Petroni, P. Gueret, J. Vigier and A. Kyprianidis, Second order wave equation for spin 1/2 fields. 2. The Hilbert space of the states, Phys. Rev. D 33 (1986) 1674 [INSPIRE].MathSciNetADSGoogle Scholar
  8. [8]
    N. Cufaro Petroni, P. Gueret and J. Vigier, Form of a spin dependent quantum potential, Phys. Rev. D 30 (1984) 495 [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    L. Hostler, An SL(2, C) invariant representation of the Dirac equation, J. Math. Phys. 23 (1982) 1179 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    L. Hostler, An SL(2, C) invariant representation of the Dirac equation. 2. Coulomb Greens function, J. Math. Phys. 24 (1983) 2366 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    L.M. Brown, Two-Component Fermion Theory, Phys. Rev. 111 (1958) 957 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    M. Tonin, Quantization of the Two-Component Fermion Theory, Nuovo Cimento 14 (1959) 1108.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    H. Pietschmann, Zur Renormierung der zweikomponentigen Quantenelektrodynamik, Acta Phys. Austriaca 14 (1961) 63.MATHGoogle Scholar
  14. [14]
    A.O. Barut and G.H. Mullen, Quantization of two-component higher order spinor equations, Ann. Phys. 20 (1962) 184.MathSciNetADSMATHCrossRefGoogle Scholar
  15. [15]
    R.Y. Volkovyskii, On the two-component theory of fermions (in Russian), Izv. Vuz. Fiz. 5 (1971)53 [Soviet Phys. J. 14 (1973) 611] [INSPIRE].Google Scholar
  16. [16]
    L. Hostler, Scalar formalism for quantum electrodynamics, J. Math. Phys. 26 (1985) 1348 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    L. Hostler, Scalar formalism for nonabelian gauge theory, J. Math. Phys. 27 (1986) 2423 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  18. [18]
    A.C. Longhitano and B. Svetitsky, Second order lattice fermions, Phys. Lett. B 126 (1983) 259 [INSPIRE].ADSGoogle Scholar
  19. [19]
    F. Palumbo, Second order formalism for fermions and lattice regularization, Nuovo Cim. A 104 (1991) 1851 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    A. Morgan, Second order fermions in gauge theories, Phys. Lett. B 351 (1995) 249 [hep-ph/9502230] [INSPIRE].ADSGoogle Scholar
  21. [21]
    M. Veltman, Two component theory and electron magnetic moment, Acta Phys. Polon. B 29 (1998)783 [hep-th/9712216] [INSPIRE].ADSGoogle Scholar
  22. [22]
    E. Delgado-Acosta, M. Napsuciale and S. Rodriguez, Second order formalism for spin 1/2 fermions and Compton scattering, Phys. Rev. D 83 (2011) 073001 [arXiv:1012.4130] [INSPIRE].ADSGoogle Scholar
  23. [23]
    K. Johnson and E. Sudarshan, Inconsistency of the local field theory of charged spin 3/2 particles, Annals Phys. 13 (1961) 126 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  24. [24]
    G. Velo and D. Zwanziger, Propagation and quantization of Rarita-Schwinger waves in an external electromagnetic potential, Phys. Rev. 186 (1969) 1337 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    G. Velo and D. Zwanziger, Noncausality and other defects of interaction lagrangians for particles with spin one and higher, Phys. Rev. 188 (1969) 2218 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M. Napsuciale, M. Kirchbach and S. Rodriguez, Spin 3/2 Beyond the Rarita-Schwinger Framework, Eur. Phys. J. A 29 (2006) 289 [hep-ph/0606308] [INSPIRE].ADSGoogle Scholar
  27. [27]
    E. Delgado-Acosta and M. Napsuciale, Compton scattering off elementary spin 3/2 particles, Phys. Rev. D 80 (2009) 054002 [arXiv:0907.1124] [INSPIRE].ADSGoogle Scholar
  28. [28]
    M. Napsuciale, S. Rodriguez, E. Delgado-Acosta and M. Kirchbach, Electromagnetic couplings of elementary vector particles, Phys. Rev. D 77 (2008) 014009 [arXiv:0711.4162] [INSPIRE].ADSGoogle Scholar
  29. [29]
    E. Delgado-Acosta, M. Kirchbach, M. Napsuciale and S. Rodriguez, Electromagnetic multipole moments of elementary spin-1/2, 1 and 3/2 particles, Phys. Rev. D 85 (2012) 116006 [arXiv:1204.5337] [INSPIRE].ADSGoogle Scholar
  30. [30]
    R. Angeles-Martinez and M. Napsuciale, Renormalization of the QED of second order spin 1/2 fermions, Phys. Rev. D 85 (2012) 076004 [arXiv:1112.1134] [INSPIRE].ADSGoogle Scholar
  31. [31]
    Y. Nambu and G. Jona-Lasinio, Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I, Phys. Rev. 122 (1961) 345 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev. 124 (1961) 246 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    A. Bondi, G. Curci, G. Paffuti and P. Rossi, Metric and central charge in the perturbative approach to two-dimensional fermionic models, Annals Phys. 199 (1990) 268 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    F. Jegerlehner, Facts of life with γ5, Eur. Phys. J. C 18 (2001) 673 [hep-th/0005255] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    J. Rafelski and L. Labun, A Cusp in QED at g = 2, arXiv:1205.1835 [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Carlos A. Vaquera-Araujo
    • 1
  • Mauro Napsuciale
    • 1
  • René Ángeles-Martınez
    • 1
  1. 1.Departamento de FísicaUniversidad de GuanajuatoGuanajuatoMéxico

Personalised recommendations