QUANTIZATION BY PARTS, MAXIMAL SYMMETRICAL OPERATORS, AND QUANTUM CIRCUITS

In the context of a generalized quantum theory which admits maximal sy mmetric operators as observables, we discuss a quantization scheme whi ch can systematically deal with what may be called quantum circuits. T he scheme, known as the method of quantization by parts, has recently been applied to obtain a new derivation of the Josephson equation for the supercurrent through a Josephson junction in a superconducting cir cuit. This paper presents an application of this scheme to several cir cuit configurations, namely, from one-branch to many-branch circuits. We also propose an experimental test on whether the condensate is alwa ys in a pure state, using a three-branch Y-shape circuit.