Finite Volume Effects in Chiral Perturbation Theory

Current knowledge suggests that the whole range of§strong interaction phenomena can be described by§quantum chromodynamics, a theory with only few§parameters. On the experimental side, the masses of§the light hadrons and many other properties are very§precisely known. On the theoretical side, it is§difficult to compute these quantities from first§principles, mainly because the coupling constant is§not small at low energies and a perturbative§expansion in this parameter can not be§carried through. §§The framework of Lattice QCD is appropriate to§address this problem on a non-perturbative level.§Introducing a finite space-time lattice and§discretizing the fields, quantitative results can§then be obtained through sophisticated numerical§simulations. However, due to the limited capacity of§today's computer systems, the lattices one is able§to simulate are rather small in size and coarse. The§extrapolation to the infinite volume limit, for§instance, is by no means straightforward. This thesis§presents a detailed analytical analysis of§finite-size effects for masses and decay constants of§the octet of pseudoscalar mesons and provides§formulae that guide the infinite-size extrapolation.