Canonical quantization of supergravity

The canonical quantization of supergravity is developed, starting from the Hamiltonian treatment of classical supergravity. Quantum states may be represented by wave functionals f(e/sup A/A' /sub i/(x),psi /sup A/ /sub i/(x)) of the spatial spinor-valued tetrad forms e/sup A/A' /sub i/ and of the right-handed spatial part psi /sup A/ /sub i/ of the spin-(3/2) field, or equivalently by functionals f(e/sup A/A' /sub i/(x),psi-bar /sup A/' /sub i/(x)) of e/sup A/A' /sub i/ and the left-handed part psi-bar /sup A/' /sub i/. In the first representation the momentum p/sub A/A' /sup i/ classically conjugate to e/sup A/A' /sub i/, together with psi-bar /sup A/' /sub i/, can be represented by functional differential operators such that the correct (anti) commutation relations hold; similarly for p/sub A/A' /sup i/,psi /sup A/ /sub i/ in the second representation. A formal inner product can be found in which p/sub A/A' /sup i/ is Hermitian and psi /sup A/ /sub i/,psi-bar /sup A/' /sub i/ are Hermitian adjoints.