%0 Journal Article %T An Interpretation of the Evidence for TeV Emission from Gamma-Ray Burst 970417a %A Tomonori Totani %J Physics %D 2000 %I arXiv %R 10.1063/1.1370889 %X The Milagrito collaboration recently reported evidence for emission of very high energy gamma-rays in the TeV range from one of the BATSE GRBs, GRB 970417a. Here I discuss possible interpretations of this result. Taking into account the intergalactic absorption of TeV gamma-rays by the cosmic infrared background, I found that the detection rate (one per 54 GRBs observed by the Milagrito) and energy fluence can be consistently explained with the redshift of this GRB at z \sim 0.7 and the isotropic total energy in the TeV range, E_{TeV, iso} >~ 10^{54} erg. This energy scale is not unreasonably large, but interestingly similar to the maximum total GRB energy observed to date, in the sub-MeV range for GRB 990123. On the other hand, the energy emitted in the ordinary sub-MeV range becomes E_{MeV, iso} \sim 10^{51} erg for the GRB 970417a, which is much smaller than the total energy in the TeV range by a factor of about 10^3. I show that the proton-synchrotron model of GRBs provides a possible explanation for these observational results. I also discuss some observational signatures expected in the future experiments from this model. %U http://arxiv.org/abs/astro-ph/0005071v1