In earlier work, the evolution operator for the exact RG equation was mapped to a field theory in Euclidean AdS. This gives a simple way of understanding AdS/CFT. We explore aspects of this map by studying a simple example of a Schrödinger equation for a free particle with time-dependent mass. This is an analytic continuation of an ERG like equation. We show for instance that it can be mapped to a harmonic oscillator. We show that the same techniques can lead to an understanding of dS/CFT too.

This paper derives the most general form of the relativistic Doppler effect and of the relativistic aberration starting from base principles available in classical electrodynamics and from the Lorentz transforms of the energy-momentum. We derive the relativistic Doppler and the relativistic aberration formulas for the case of both source and receiver moving in arbitrary directions with respect to an inertial reference frame as viewed from either a uniformly rotating or a uniformly accelerated frame.