Restrictions on ground state average values imposed by time reversal symmetry

Time reversal symmetry is applied in the following cases. (a) On the ground state expectation values of the product of two or three Hermitian operators in order to get some new rules: depending on their T-symmetry the expectation value of the commutator or anticommutator (or a function of them) will vanish. (b) On polarization propagators: by enforcing a simple time reversal relationship between advanced and retarded propagators the strong condition is found that the operators used must have the same time reversal symmetry. This condition generalizes another well known condition which relates the ‘reality’ of the operators with their spin symmetry. Some examples are given for both applications.