Non-Perturbative Effects of Strong Magnetic Fields on Neutrino Self-energy: A New Approach∗

The Ritus’ Ep eigenfunction method is extended to the case of spin-1 charged particles in a constant electromagnetic field and used to calculate the one-loop neutrino self-energy in the strong-field approximation me ≪ eB ≪ M2 W . The implications of the obtained results for neutrino oscillations in the early Universe, assuming the existence of a sufficiently large (me ≪ eB ≪ mμ) primordial magnetic field, are discussed. The diagonalization, structure and properties of the Green’s functions of the electron and photon in an intense magnetic field were considered exactly in external and radiative fields by Ritus in Refs. [1] and [2]. Ritus’ formulation provides an alternative method to the Schwinger approach to address QFT problems on electromagnetic backgrounds. In Ritus’ approach the transformation to momentum space of the spin-1/2 particle Green’s function in the presence of a constant magnetic field is carried out using the Ep(x) functions[1],[2] corresponding to the eigenfunctions of the spin-1/2 charged particles in the electromagnetic background. The Ep(x) functions plays the role, in the presence of magnetic fields, of the usual Fourier e functions of the free case. This method is very convenient for strong-field calculations, ∗Talk given at the International Conference ”Quantization, Gauge Theory and Strings” dedicated to the memory of Prof. Efim Fradkin; Moscow, Jun. 5-10, 2000