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We review the Exact Renormalization Group equations of Wegner and Houghton in an approximation which permits both numerical and analytical studies of nonperturbative renormalization flows. We obtain critical exponents numerically and with the local polynomial approximation (LPA), and discuss the advantages and shortcomings of these methods, and compare our(More)
We present a proof of the irreversibility of renormalization group flows, i.e. the c–theorem for unitary, renormalizable theories in four (or generally even) dimensions. Using Ward identities for scale transformations and spectral representation arguments, we show that the c–function based on the trace of the energy-momentum tensor (originally suggested by(More)
Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories. Renormalization group equations and their solutions are amenable to a simple formulation which is manifestly covariant(More)
The pixel values of an image can be casted into a real ket of a Hilbert space using an appropriate block structured addressing. The resulting state can then be rewritten in terms of its matrix product state representation in such a way that quantum entanglement corresponds to classical correlations between different coarse-grained textures. A truncation of(More)
We construct a parametrization of the deep-inelastic structure function of the proton F 2 (x, Q 2) based on all available experimental information from charged lepton deep-inelastic scattering experiments. The parametrization effectively provides a bias-free determination of the probability measure in the space of structure functions, which retains(More)
We present the determination of a set of parton distributions of the nucleon, at next-to-leading order, from a global set of deep-inelastic scattering data: NNPDF1.0. The determination is based on a Monte Carlo approach, with neural networks used as unbiased interpolants. This method, previously discussed by us and applied to a determination of the(More)
The Gauss law constraint in the Hamiltonian form of the SU (2) gauge theory of gluons is satisfied by any functional of the gauge invariant tensor variable φ ij = B ia B ja. Arguments are given that the tensor G ij = (φ −1) ij det B is a more appropriate variable. When the Hamiltonian is expressed in terms of φ or G, the quantity Γ i jk appears. The gauge(More)