On Functional Integral Representations Satisfying the Constraints in the Correlation Models of High‐Temperature Superconductors

Functional integral representations are constructed for Fermions with spin 1/2, in which the fields satisfy directly by construction the constraints (e.g., exclusion of double occupancy of a site) appearing in recent models in the theory of high‐temperature superconductivity. Thus, the enforcement of the constraints by delta functions in the integration measure is avoided. Perelomov's concept of generalized coherent states is used. However, in constructing such representations, exponential functions of linear combinations of operators (which are difficult to disentangle) are avoided, as is the construction and reduction of the invariant measure. Instead, an ansatz is used for the resolution of the unity operator. This approach also provides more freedom in choosing the appropriate fields. Several new and simple representations with only few elementary fields are given. The representation already used by Wiegmann is recovered. In this case and in any other cases the integration measure is explicitly given. In all these representations, the original Fermi operators are substituted by the product of a spin independent Graßmann field and a spin dependent bosonic (complex) field in accordance with the physical idea of separation of charge and spin degrees of freedom. It is further shown how a change in the integration measure eliminates also zero occupancy (the case of the Heisenberg antiferromagnet). The absence of an explicit delta function constraint in the functional integral is reflected in a special form of the kinetic part of the action. The considered representations are compared with that of the slave boson method.