  In the talk, I briefly demonstrate the quantum theory for mesoscopic electric
circuits and its applications. In the theory, the importance of the charge
discreteness in a mesoscopic electric circuit is addressed. As a result, a new
kind of commutation relation for electric charge and current occurred
inevitably. The charge representation, canonical current representation and
pseudo-current representation are discussed extensively. It not only provides a
concrete realization of mathematical models which discuss the space
quantization in high energy physics and quantum gravity but also presents a
sequence of applications in condensed matter physics from a different point of
view. A possible generalization to coupled circuits is also proposed.
