The tree-level two-point amplitudes for the transitions $jf to j^{, prime} f^{, prime}$, where $f$ is a fermion and $j$ is a generalized current, in a constant uniform magnetic field of an arbitrary strength and in charged fermion plasma, for the $jf
$ interaction vertices of the scalar, pseudoscalar, vector and axial-vector types have been investigated. The particular cases of a very strong magnetic field, and of the coherent scattering off the real fermions without change of their states (the forward scattering) have been analysed.
Results of a partial wave analysis of new high-statistics data on $gamma pto peta$ from MAMI are presented. A fit using known broad resonances and only standard background amplitudes can not describe the relatively narrow peaking structure in the cro
ss section in the mass region of 1660-1750 MeV which follows a minimum. An improved description of the data can be reached by either assuming the existence of a narrow resonance at a mass of about 1700 MeV with small photo-coupling or by a threshold effect. In the latter case the observed structure is explained by a strong (resonant or non-resonant) $gamma ptoomega p$ coupling in the $S_{11}$ partial wave. When the beam asymmetry data, published by part of the GRAAL collaboration, are included in the fit, the solution with a narrow $P_{11}$ state is slightly preferred. In that fit, mass and width of the hypothetical resonance are determined to $Msim$1694 MeV and $Gammasim 40$ MeV, respectively, and the photo-coupling to $sqrt{{rm Br}_{eta N}} A_{1/2}^p sim 2.6cdot 10^{-3}$ GeV$^{-1/2}$. High precision measurements of the target asymmetry and $F$-observable are mandatory to establish the possible existence of such a narrow state and to provide the necessary information to define which partial wave is responsible for the structure observed in the data.
The first study of quasi-free Compton scattering on the neutron in the energy range of $E_{gamma}=0.75 - 1.5$ GeV is presented. The data reveals a narrow peak at $Wsim 1.685$ GeV. This result, being considered in conjunction with the recent evidence
for a narrow structure at $Wsim 1.68$GeV in the $eta$ photoproduction on the neutron, suggests the existence of a new nucleon resonance with unusual properties: the mass $Msim 1.685$GeV, the narrow width $Gamma leq 30$MeV, and the much stronger photoexcitation on the neutron than on the proton.
