Quantum states and the Hadamard form. I. Energy minimization for scalar fields

We investigate properties of the states of a scalar field in a Robertson-Walker space-time constructed by an energy-minimization requirement. It is shown that in general the anticommutator expectation value 〈^Φ(x)^Φ(x^')+^Φ(x^')^Φ(x)〉 of these states will not possess the Hadamard form. We present a simple example in which we can give a closed form for such an expectation value. The implications of this result for renormalization theory in quantum field theory on curved space-time are discussed.