The functional Schroedinger representation developed earlier for elementary particle physics has been rarely employed for the study of condensed matter and statstical physics. In the present study, we study the two-dimensional antiferromagnetic systems of strongly correlated electrons by paying attention to the Schroedinger representations of different statistical approaches, namely, the Holstein-Primakoff theory and the slave-boson theory of the t-J Hamiltonian. From this study, interrelationships between these theories are presented. At half-filling, the dispersion relation obtained from the more generalized slave-boson theory is shown to reduce to that obtained from the Holstein-Primakoff boson theory. By using the functional Schroedinger representation of the generalized Holstein-Primakoff theory, we further show that the ground state energy is lowered by the self-energy of a quasi-hole owing to the presence of coupling between the holon and the magnon.
Functional Schroedinger representation; Two-dimensional antiferromagnetic systems of strongly correlated electrons; Slave-boson theory; Holstein-Primakoff boson theory