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spectral theory --- partial differential equations --- mathematical physics --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics)

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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

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Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories.

Research & information: general --- Physics --- semiheaps --- ternary algebras --- para-associativity --- quantum mechanics --- gravity --- Clairaut equation --- Cho–Duan–Ge decomposition --- constraintless formalism --- canonical gravity --- covariance --- black holes --- quantum foundations --- non-axiomaticity --- detector clicks --- ensembles --- superposition principle --- arithmetic --- numbers --- vector space --- abstracting --- interpretations --- self-referentiality --- direct product --- direct power --- polyadic semigroup --- arity --- polyadic ring --- polyadic field --- Maxwell’s vacuum equations --- Hamilton–Jacobi equation --- Klein–Gordon–Fock equation --- algebra of symmetry operators --- separation of variables --- linear partial differential equations --- Einstein field equation --- recursion operator --- Noether symmetry --- master symmetry --- conformable differential --- Poisson manifold --- diffeomorphism group --- current algebra symmetry --- current Lie algebra representation --- fock space --- generating functional --- distribution functions --- Lie–Poisson structure --- coherent states --- Lie-Poisson action --- Hilbert space linearization --- hamiltonian systems --- symmetry reduction --- integrability --- idiabatic states --- factorization --- heavenly type dynamical systems --- integrable dynamical systems --- dirac reduction --- hydrodynamic flows --- entropy --- vortex flows --- asymptotic conditions --- Kirchhoff’s integral theorem --- quantum gravity and the problem of the Big Bang --- hidden Hermitian formulations of quantum mechanics --- stationary Wheeler-DeWitt system --- physical Hilbert space metric --- non-stationary Wheeler-DeWitt system --- n/a --- Cho-Duan-Ge decomposition --- Maxwell's vacuum equations --- Hamilton-Jacobi equation --- Klein-Gordon-Fock equation --- Lie-Poisson structure --- Kirchhoff's integral theorem

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This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.

Equacions d'evolució --- Equacions en derivades parcials --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Open Access --- Evolutionary equations --- Maxwell's equations --- Initial Boundary Value Problems --- Mathematical Physics --- Hilbert space approach --- Heat Equation --- Wave Equation --- Elasticity --- Differential Algebraic Equations --- Exponential Stability --- Homogenisation --- Evolutionary Inclusions --- Time-dependent partial differential equations --- Coupled Systems --- Causality --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Kármán --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica)

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Computational intelligence is a general term for a class of algorithms designed by nature's wisdom and human intelligence. Computer scientists have proposed many computational intelligence algorithms with heuristic features. These algorithms either mimic the evolutionary processes of the biological world, mimic the physiological structure and bodily functions of the organism,

individual updating strategy --- integrated design --- global optimum --- flexible job shop scheduling problem --- whale optimization algorithm --- EHO --- bat algorithm with multiple strategy coupling (mixBA) --- multi-objective DV-Hop localization algorithm --- optimization --- rock types --- variable neighborhood search --- biology --- average iteration times --- CEC2013 benchmarks --- slicing tree structure --- firefly algorithm (FA) --- benchmark --- single loop --- evolutionary computation --- memetic algorithm --- normal cloud model --- 0-1 knapsack problems --- elite strategy --- diversity maintenance --- material handling path --- artificial bee colony algorithm (ABC) --- urban design --- entropy --- evolutionary algorithms (EAs) --- monarch butterfly optimization --- numerical simulation --- architecture --- set-union knapsack problem --- Wilcoxon test --- convolutional neural network --- global position updating operator --- particle swarm optimization --- computation --- minimum load coloring --- topology structure --- adaptive multi-swarm --- minimum total dominating set --- mutation operation --- shape grammar --- greedy optimization algorithm --- ?-Hilbert space --- genetic algorithm --- large scale optimization --- large-scale optimization --- NSGA-II-DV-Hop --- constrained optimization problems (COPs) --- first-arrival picking --- transfer function --- SPEA 2 --- stochastic ranking (SR) --- wireless sensor networks (WSNs) --- acceleration search --- convergence point --- fuzzy c-means --- evolutionary algorithm --- success rates --- Artificial bee colony --- particle swarm optimizer --- random weight --- range detection --- adaptive weight --- large-scale --- automatic identification --- cloud model --- swarm intelligence --- evolutionary multi-objective optimization --- DV-Hop algorithm --- bat algorithm (BA) --- Friedman test --- quantum uncertainty property --- facility layout design --- local search --- deep learning --- Y conditional cloud generator --- benchmark functions --- discrete algorithm --- dispatching rule --- DE algorithm --- nonlinear convergence factor --- energy-efficient job shop scheduling --- t-test --- evolution --- dimension learning --- global optimization --- confidence term --- elephant herding optimization --- moth search algorithm --- evolutionary