Second order formalism for spin 1/2 fermions and Compton scattering

Abstract

We develop a second order formalism for spin 1/2 fermions based on the projection over Poincaré invariant subspaces in the $(1/2,0)\oplus (0,1/2)$ representation of the homogeneous Lorentz group. Using $U(1{)}_{em}$ gauge principle we obtain second order description for the electromagnetic interactions of a spin 1/2 fermion with two free parameters, the gyromagnetic factor $g$ and a parameter $\xi$ related to odd-parity Lorentz structures. We calculate Compton scattering in this formalism. In the particular case $g=2,\xi =0$ and for states with well defined parity we recover Dirac results. In general, we find the correct classical limit and a finite value $r_c^2$ for the forward differential cross section, independent of the photon energy and of the value of the parameters $g$ and $\xi$. The differential cross section vanishes at high energies for all $g,\xi$ except in the forward direction. The total cross section at high energies vanishes only for $g=2,\xi =0$. We argue that this formalism is more convenient than Dirac theory in the description of low energy electromagnetic properties of baryons and illustrate the point with the proton case.

11 pages 4 figures

References in corpus (9)

• Measurement of charged current triple gauge boson couplings using W pairs at LEP
• Measurement of Triple-Gauge-Boson Couplings of the W Boson at LEP
• Spin 3/2 Beyond the Rarita-Schwinger Framework
• Measurement of Trilinear Gauge Boson Couplings WWV, (V = Z,gamma) in e+e- Collisions at 189 GeV
• Measurements of CP-conserving Trilinear Gauge Boson Couplings WWV (V = gamma,Z) in e+e- Collisions at LEP2
• Factorization in Graviton Scattering and the "Natural" Value of the g-factor
• How Large is the "Natural" Magnetic Moment?
• Compton scattering off elementary spin 3/2 particles
• Electromagnetic couplings of elementary vector particles

Cited by in corpus (8)

• Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes
• Magnetic Dipole Moment in Relativistic Quantum Mechanics
• Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory
• Renormalization of the QED of second order spin 1/2 fermions
• Electromagnetic multipole moments of elementary spin-1/2, 1, and 3/2 particles
• Compton scattering off massive fundamental bosons of pure spin 1
• Gyromagnetic g_s factors of the spin-1/2 particles in the (1/2+,1/2-,3/2-) triad of the four-vector spinor, ψ_μ, irreducibility, and linearity
• Second order theory of $(j,0)\oplus (0,j)$ single high spins as Lorentz tensors