Skip to Main Content

Access Provided by Xinjiang University

Physical Review D

Access by Xinjiang University

Renormalization of the QED of second-order spin $\frac{1}{2}$ fermions

René Ángeles-Martínez and Mauro Napsuciale

Departamento de Física, Universidad de Guanajuato, Lomas del Campestre 103 and Fraccionamiento Lomas del Campestre, León, Guanajuato México, 37150

Phys. Rev. D 85, 076004 – Published 5 April, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.076004

Abstract

In this work we study the renormalization of the electrodynamics of spin $1 / 2$ fermions in the Poincaré projector formalism which is second order in the derivatives of the fields. We analyze the superficial degree of divergence of the vertex functions of this theory, and calculate at one-loop level the vacuum polarization, fermion self-energy, and $γ$ -fermion-fermion vertex function, and the divergent piece of the one-loop contributions to the $γ$ - $γ$ -fermion-fermion vertex function. It is shown that these functions are renormalizable independently of the value of the gyromagnetic factor $g$ , which is a free parameter of the theory. We find a photon propagator and a running coupling constant $α (q^{2})$ that depend on the value of $g$ . The magnetic moment form factor contains a divergence associated with $g$ , which disappears for $g = 2$ but, in general, requires the coupling $g$ to be renormalized. A suitable choice of the renormalization condition for the magnetic form factor yields the one-loop finite correction $Δ g = g α / 2 π$ . For a particle with $g = 2$ we recover results of Dirac theory for the photon propagator, the running of $α (q^{2})$ , and the one-loop corrections to the gyromagnetic factor.

See Also

Compton scattering off elementary spin $\frac{3}{2}$ particles

E. G. Delgado-Acosta and M. Napsuciale

Phys. Rev. D 80, 054002 (2009)

Article Text

References (27)

K. Johnson and E. C. Sudarshan, Ann. Phys. (N.Y.) 13, 126 (1961); G. Velo and D. Zwanziger, Phys. Rev. 186, 1337 (1969); 188, 2218 (1969).
M. Napsuciale, M. Kirchbach, and S. Rodriguez, Eur. Phys. J. A 29, 289 (2006).
E. G. Delgado-Acosta and M. Napsuciale, Phys. Rev. D 80, 054002 (2009).
M. Napsuciale, S. Rodriguez, E. G. Delgado-Acosta, and M. Kirchbach, Phys. Rev. D 77, 014009 (2008).
E. G. Delgado-Acosta, M. Napsuciale, and S. Rodriguez, Phys. Rev. D 83, 073001 (2011).
R. P. Feynman, Phys. Rev. 84, 108 (1951).
V. Fock, Phys. Z. Sowjetunion 12, 404 (1937).
R. P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958).
C. Schubert, Phys. Rep. 355, 73 (2001).
L. C. Biedenharn, M. Y. Han, and H. Van Dam, Phys. Rev. D 6, 500 (1972).
N. Cufaro Petroni, P. Gueret, J. P. Vigier, and A. Kyprianidis, Phys. Rev. D 31, 3157 (1985); 33, 1674 (1986).
N. Cufaro Petroni, P. Gueret, and J. P. Vigier, Phys. Rev. D 30, 495 (1984).
L. C. Hostler, J. Math. Phys. (N.Y.) 23, 1179 (1982).
L. C. Hostler, J. Math. Phys. (N.Y.) 24, 2366 (1983).
L. M. Brown, Phys. Rev. 111, 957 (1958).
M. Tonin, Nuovo Cimento, 14, 1108 (1959).
H. Pietschmann, Acta Phys. Austriaca 14, 63 (1961).
A. O. Barut and G. H. Mullen, Ann. Phys. (N.Y.) 20, 184 (1962).
R. Y. Volkovyskii, Izv. Vuz. Fiz. 5, 53 (1971) [Russ. Phys. J. 14, 611 (1973)].
L. C. Hostler, J. Math. Phys. (N.Y.) 26, 1348 (1985).
L. C. Hostler, J. Math. Phys. (N.Y.) 27, 2423 (1986).
A. C. Longhitano and B. Svetitsky, Phys. Lett. 126B, 259 (1983).
F. Palumbo, Nuovo Cimento Soc. Ital. Fis. A 104, 1851 (1991).
A. G. Morgan, Phys. Lett. B 351, 249 (1995).
M. J. G. Veltman, Acta Phys. Pol. B 29, 783 (1998).
R. Mertig, http://www.feyncalc.org.
M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995).