  While the fluorescence and the ground counter techniques for the detection of
ultra-high energy cosmic rays (UHECR) were being developed for decades, the
interest in the radio detection diminished after the initial experiments in the
1960s. As a result, the fluorescence and the surface array techniques are more
mature today, providing more reliable measurements of the primary cosmic
particle energy, chemical composition and the inelastic cross-section. The
advantages of the radio technique are 100 percent duty cycle and lower
deployment and operational costs. Thus, the radio technique can greatly
complement the fluorescence and the ground array detection and can also work
independently. With the ANITA balloon detector observing UHECRs and the success
of LOPES, CODALEMA and other surface radio detectors, the radio technique
received a significant boost in recent years. Reliable Monte Carlo (MC)
simulations are needed in order to obtain the energy and other parameters of
the primary cosmic ray particle from the radio observations. Several MC
techniques, like ZHairesS and the Endpoint Formalism, were proposed in recent
years. While they seem to reproduce some of the observed data quite well, there
is a divergence between the different approaches under certain conditions. In
this work we derive these approaches from Maxwells equations and prove their
identity under certain conditions as well as discuss their applicability to the
UHECR air showers and to a proposed experiment at SLAC.
