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Intensive studies on light–matter interactions and technological breakthroughs, especially conducted in the field of dressed photon research, have led to a growing concern regarding unsettled off-shell quantum field interactions. The Special Issue, entitled “Quantum Fields and Off-Shell Sciences”, was organized to promote the progress of such research activities from a wider perspective, not limited to dressed photon studies. This book contains excellent papers that were published in this Special Issue. It will provide scientific and technical information on the quantum fields and off-shell sciences to scientists, engineers, and students who are and will be engaged in this field.
Research & information: general --- Physics --- dressed photon --- dressed photon constant --- natural units --- Heisenberg cut --- de Sitter space --- dark energy --- dark matter --- cosmological constant --- twin universes --- conformal cyclic cosmology --- quantum walk --- scattering theory --- energy --- survival probability --- attractor eigenspace --- category --- algebra --- state --- category algebra --- state on category --- noncommutative probability --- quantum probability --- GNS representation --- quantum measurement --- C*-algebra --- algebraic quantum field theory --- local net --- extension of local net --- completely positive instrument --- macroscopic distinguishability --- Grassmann manifold --- flag manifold --- pre-homogeneous vector space --- invariants --- category theory --- nonstandard analysis --- coarse geometry --- quantum field --- combinatorial optimization --- Ising spin glass --- coupled oscillator --- eigenmode --- clustering --- localization --- dissipation --- off-shell science --- non-equilibrium open system --- quantum master equation --- quantum density matrix --- projection operator --- renormalization --- discrete-time quantum walk --- scattering quantum random walk --- Grover walk --- pathfinding --- network
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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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