Gauge symmetry breaking, collective modes, and boson superconductivity in the t-J model

A theory of the t-J model in the presence of an external electromagnetic field is presented. The 1/N expansion for this model in the slave-fermion representation is developed, and it is shown that all the general properties of the theory are satisfied in every order of the 1/N expansion separately. A convenient procedure of the gauge fixing is suggested. It is shown that superconductivity may exist in this model even in the absence of the electron pairing. It is argued that experimental predictions of the theory might agree with the observed properties of the copper oxides.