Finite temperature expectation values of boundary operators

A conjecture is presented for the thermal one-point function of boundary operators in integrable boundary quantum field theories in terms of form factors. It is expected to have applications in studying boundary critical phenomena and boundary flows, which are relevant in the context of condensed matter and string theory. The conjectured formula is verified by a low-temperature expansion developed using finite size techniques, which can also be used to evaluate higher point functions both in the bulk and on the boundary.