LOCAL GAUGE-INVARIANCE VERSUS SLAVE BOSON-LIKE REPRESENTATIONS IN SYSTEMS WITH STRONGLY CORRELATED ELECTRONS

The flux phase solutions in the t-J model the gauge theories with Cher n-Simons term, promising new exciting physics, are so far obtained onl y within slave-boson (or fermion) approaches, where local gauge invari ance is not taken into account exactly. We inspect the possibility to do this, mainly, in the example of the t-J model The analysis of diffe rent parametrizations in the functional representation shows that (i) calculations which take into account constraints for the number of on- site-available states are describing quasiparticles in terms of the wr ong local statistics, and contain gauge non-invariant objects; (ii) ap plication of the projection technique in the slave-boson(fermion) repr esentation reproduces the correct statistics, and is exactly equivalen t to the conventional diagram technique for Hubbard operators. In the language of slave bosons this means that the Fourier transformation le ading to Bloch states should be made only after accounting constraints in the measure of functional integral.