TY - BOOK ID - 113601486 TI - Selected Topics in Gravity, Field Theory and Quantum Mechanics AU - Duplij, Steven AU - Walker, Michael L. PY - 2022 SN - 303655906X 3036559051 PB - Basel MDPI - Multidisciplinary Digital Publishing Institute DB - UniCat KW - Research & information: general KW - Physics KW - semiheaps KW - ternary algebras KW - para-associativity KW - quantum mechanics KW - gravity KW - Clairaut equation KW - Cho–Duan–Ge decomposition KW - constraintless formalism KW - canonical gravity KW - covariance KW - black holes KW - quantum foundations KW - non-axiomaticity KW - detector clicks KW - ensembles KW - superposition principle KW - arithmetic KW - numbers KW - vector space KW - abstracting KW - interpretations KW - self-referentiality KW - direct product KW - direct power KW - polyadic semigroup KW - arity KW - polyadic ring KW - polyadic field KW - Maxwell’s vacuum equations KW - Hamilton–Jacobi equation KW - Klein–Gordon–Fock equation KW - algebra of symmetry operators KW - separation of variables KW - linear partial differential equations KW - Einstein field equation KW - recursion operator KW - Noether symmetry KW - master symmetry KW - conformable differential KW - Poisson manifold KW - diffeomorphism group KW - current algebra symmetry KW - current Lie algebra representation KW - fock space KW - generating functional KW - distribution functions KW - Lie–Poisson structure KW - coherent states KW - Lie-Poisson action KW - Hilbert space linearization KW - hamiltonian systems KW - symmetry reduction KW - integrability KW - idiabatic states KW - factorization KW - heavenly type dynamical systems KW - integrable dynamical systems KW - dirac reduction KW - hydrodynamic flows KW - entropy KW - vortex flows KW - asymptotic conditions KW - Kirchhoff’s integral theorem KW - quantum gravity and the problem of the Big Bang KW - hidden Hermitian formulations of quantum mechanics KW - stationary Wheeler-DeWitt system KW - physical Hilbert space metric KW - non-stationary Wheeler-DeWitt system KW - n/a KW - Cho-Duan-Ge decomposition KW - Maxwell's vacuum equations KW - Hamilton-Jacobi equation KW - Klein-Gordon-Fock equation KW - Lie-Poisson structure KW - Kirchhoff's integral theorem UR - https://www.unicat.be/uniCat?func=search&query=sysid:113601486 AB - 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. ER -