We show that the quantum properties of some Josephson SQUID devices are
described by a boundary sine Gordon model. Our approach naturally describes
multi-junction SQUID devices and, when applied to a single junction SQUID (the
rf-SQUID), it reproduces the known results of Glazman and Hekking. We provide a
detailed analysis of the regimes accessible to an rf-SQUID and to a
two-Josephson junction SQUID device (the dc-SQUID). We then compute the normal
component of the current-response of a SQUID device to an externally applied
voltage and show that the equation describing the current-voltage
characteristic function reduces to well-known results when the infrared cutoff
is suitably chosen. Our approach helps in establishing new and interesting
connections between superconducting devices, quantum brownian motion, fermionic
quantum wires and, more generally, quantum impurity problems.Comment: 54 pages, 1 figure, 1 section added, new figur