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This book celebrates the 80 years of the Professor Eugene P. Wigner paper “On Unitary Representations of the Inhomogeneous Lorentz Group", published in The Annals of Mathematics in 1939. We have collected several contributions divided into Research articles and Reviews. All contributions are technical, but the papers also bring a health element of didactic. Practitioners from several areas, from Gravity to Quantum Field Theory and Quantum Mechanics, as well as students, shall find a rich material in this Volume.

spinors in 4d --- regularization --- anomalies --- quantum gravity --- quantum mechanics --- symmetry --- quantum cosmology --- special relativity --- combination of velocities --- wigner angle --- quaternions --- gauge field theory --- Yang-Mills fields --- modified gravity --- non-Riemannian geometry --- spacetime symmetries --- gauge field theories --- gauge anomalies --- nonperturbative techniques --- ray representation --- strongly continuous --- continuity --- Hilbert space --- entanglement --- bispinors --- chirality --- n/a