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Do humans have a free choice of which actions to perform? Three recent developments of modern science can help us to answer this question. First, new investigative tools have enabled us to study the processes in our brains which accompanying our decisions. The pioneer work of Benjamin Libet has led many neuroscientists to hold the view that our conscious intentions do not cause our bodily movements but merely accompany them. Then, Quantum Theory suggests that not all physical events are fully determined by their causes, and so opens the possibility that not all brain events may be fully determined by their causes, and so maybe — if neuroscience does not rule this out — there is a role for intentions after all. Finally, a theorem of mathematics, Gödel's theory, has been interpreted to suggest that the initial conditions and laws of development of a mathematician's brain could not fully determine which mathematical conjectures he sees to be true. The extent to which human behaviour is determined by brain events may well depend on whether conscious events, such as intentions, are themselves merely brain events, or whether they are separate events which interact with brain events (perhaps in the radical form that intentions are events in our soul, and not in our body). This book considers what kind of free will we need in order to be morally responsible for our actions or be held guilty in a court of law. Is it sufficient merely that our actions are uncaused by brain events?

The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. students and postdoctoral Fellows with the principles and methods of modern lattice field theory, which Is set to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations. The emphasis of the book is on the theoretical developments that have shaped the field in the last two decades and that have turned lattice gauge theory into a robust approach to the determination of low energy hadronic quantities and of fundamental parameters of the Standard Model. By way of introduction, the courses of the school began by covering lattice theory basics (P. Hernández), lattice renormalization and improvement (P. Weisz and A. Vladikas) and the many faces of chirality (D.B. Kaplan). A later course introduced QCD at finite temperature and density (O. Philipsen). A broad view of lattice computation from the basics to recent developments was offered in the corresponding course (M. Lüscher). The students learned the basics of lattice computation in a hands-on tutorial (S. Schaefer)---a first at Les Houches, Extrapolations to physical quark masses and a framework for the parameterization of the low-energy physics by means of effective coupling constants has been covered in the course on chiral perturbation theory (M. Golterman). A course in heavy-quark effective theories (R. Sommer), an essential tool for performing the relevant lattice calculations, covered HQET from its basics to recent advances. A number of shorter courses rounded out the school and broadened its purview. These included recent applications to flavour physics (L. Lellouch) the nucleon--nucleon interation (S. Aoki) and a course on physics beyond the Standard Model (T. Appelquist and E.T. Neil).