  We theoretically and phenomenologically investigate the question whether the
gamma-ray emission from the remnants of the type Ia supernovae SN 1006, Tycho's
SN and Kepler's SN can be the result of electron acceleration alone. The
observed synchrotron spectra of the three remnants are used to determine the
average momentum distribution of nonthermal electrons as a function of the
assumed magnetic field strength. Then the inverse Compton emission spectrum in
the Cosmic Microwave Background photon field is calculated and compared with
the existing upper limits for the very high energy gamma-ray flux from these
sources. It is shown that the expected interstellar magnetic fields
substantially overpredict even these gamma-ray upper limits. Only rather
strongly amplified magnetic fields could be compatible with such low gamma-ray
fluxes. However this would require a strong component of accelerated nuclear
particles whose energy density substantially exceeds that of the synchrotron
electrons, compatible with existing theoretical acceleration models for nuclear
particles and electrons. Even though the quantitative arguments are simplistic,
they appear to eliminate simplistic phenomenological claims in favor of a
inverse Compton gamma-ray scenario for these sources.
