  The principal paradigm for gamma-ray bursts (GRBs) suggests that the prompt
transient gamma-ray signal arises from multiple shocks internal to the
relativistic expansion. This paper explores how GRB prompt emission spectra can
constrain electron (or ion) acceleration properties at the relativistic shocks
that pertain to GRB models. The array of possible high-energy power-law indices
in accelerated populations is highlighted, focusing on how spectra above 1 MeV
can probe the field obliquity in GRB internal shocks, and the character of
hydromagnetic turbulence in their environs. When encompassing the MeV-band
spectral break, fits to BATSE/EGRET burst data indicate that the preponderance
of electrons responsible for the prompt emission reside in an intrinsically
non-thermal population. This differs markedly from typical populations
generated in acceleration simulations; potential resolutions of this conflict
such as the action of self-absorption are mentioned. Spectral modeling also
suggests that the synchrotron mechanism is favored over synchrotron
self-Compton scenarios due to the latter's typically broad curvature near the
peak. Such diagnostics will be enhanced by the broadband spectral coverage of
bursts by the Fermi Gamma-Ray Space Telescope; the GBM will provide key
information on the lower energy portions of the non-thermal particle
population, while the LAT will constrain the power-law regime of particle
acceleration.

High Energy Astrophysical Phenomena