In this thesis we investigate finite size effects in 1+1 dimensional integrable QFT. In particular we consider matrix elements of local operators (finite volume form factors) and vacuum expectation values and correlation functions at finite temperature. In the first part of the thesis we give a complete description of the finite volume form factors in terms of the infinite volume form factors (solutions of the bootstrap program) and the S-matrix of the theory. The calculations are correct to all orders in the inverse of the volume, only exponentially decaying (residual) finite size effects are neglected. We also consider matrix elements with disconnected pieces and determine the general rule for evaluating such contributions in a finite volume. The analytic results are tested against numerical data obtained by the truncated conformal space approach in the Lee-Yang model and the Ising model in a magnetic field. In a separate section we also evaluate the leading exponential correction (the
μ-term) associated to multi-particle energies and matrix elements. In the second part of the thesis we show that finite volume factors can be used to derive a systematic low-temperature expansion for correlation functions at finite temperature. In the case of vacuum expectation values the series is worked out up to the third non-trivial order and a complete agreement with the LeClair-Mussardo formula is observed. A preliminary treatment of the two-point function is also given by considering the first nontrivial contributions.
We study the finite-temperature expectation values of exponential fields in the sine-Gordon model. Using finite-volume regularization, we give a low-temperature expansion of such quantities in terms of the connected diagonal matrix elements, for which we provide explicit formulas. For special values of the exponent, computations by other methods are available and used to validate our findings. Our results can also be interpreted as a further support for a previous conjecture about the connection between finite-and infinite-volume form factors valid up to terms exponentially decaying in the volume.