Ashtekar's formalism in first-order tetrad form

Ashtekar's polynomial constraints for a new canonical gravity are examined in the first-order tetrad formalism. The action is given by the sum of Einstein's action and a complex total divergence term. We find the canonical form of the Hamiltonian explicitly. In the Hamiltonian, the coefficients of Gauss-law constraints are not arbitrary functions but must satisfy nonpolynomial relations. They guarantee the reality condition of canonical variables. In quantum theory an additional measure factor must be required in the inner product of state space.