  A simple diffeomorphism invariant theory of connections with the non-compact
structure group R of real numbers is quantized. The theory is defined on a
four-dimensional 'space-time' by an action resembling closely the self-dual
Plebanski action for general relativity. The space of quantum states is
constructed by means of projective techniques by Kijowski. Except this point
the applied quantization procedure is based on Loop Quantum Gravity methods.
