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The two-dimensional Hubbard model for interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the high-Tc cuprates. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom, bosonic fields are introduced which correspond to different collective orders, for example magnetism and superconductivity. The interactions between bosons and fermions are ...

If the laws of nature are fine-tuned for life, can we infer other universes with different laws? How could we even test such a theory without empirical access to those distant places? Can we believe in the multiverse of the Everett interpretation of quantum theory or in the reality of other possible worlds, as advocated by philosopher David Lewis? At the intersection of physics and philosophy of science, this book outlines the philosophical challenge to theoretical physics in a measured, well-grounded manner. The origin of multiverse theories are explored within the context of the fine-tuning...