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Selected Topics in Gravity, Field Theory and Quantum Mechanics
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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.
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Keywords
- Abstracting
- algebra of symmetry operators
- Arithmetic
- arity
- asymptotic conditions
- black holes
- canonical gravity
- Cho–Duan–Ge decomposition
- Clairaut equation
- coherent states
- conformable differential
- constraintless formalism
- covariance
- current algebra symmetry
- current Lie algebra representation
- detector clicks
- diffeomorphism group
- dirac reduction
- direct power
- direct product
- distribution functions
- Einstein field equation
- ensembles
- Entropy
- Factorization
- fock space
- generating functional
- gravity
- Hamiltonian systems
- Hamilton–Jacobi equation
- heavenly type dynamical systems
- hidden Hermitian formulations of quantum mechanics
- Hilbert space linearization
- hydrodynamic flows
- idiabatic states
- integrability
- integrable dynamical systems
- interpretations
- Kirchhoff’s integral theorem
- Klein–Gordon–Fock equation
- Lie-Poisson action
- Lie–Poisson structure
- linear partial differential equations
- master symmetry
- Mathematics & science
- Maxwell’s vacuum equations
- n/a
- Noether symmetry
- non-axiomaticity
- non-stationary Wheeler-DeWitt system
- Numbers
- para-associativity
- physical Hilbert space metric
- Physics
- Poisson manifold
- polyadic field
- polyadic ring
- polyadic semigroup
- quantum foundations
- quantum gravity and the problem of the Big Bang
- quantum mechanics
- recursion operator
- Reference, information & interdisciplinary subjects
- Research & information: general
- self-referentiality
- semiheaps
- Separation Of Variables
- stationary Wheeler-DeWitt system
- superposition principle
- symmetry reduction
- ternary algebras
- vector space
- vortex flows
Links
DOI: 10.3390/books978-3-0365-5906-3Editions