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Selected Topics in Gravity, Field Theory and Quantum Mechanics

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...

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Enregistré dans:
Format: Online
Langue:anglais
Publié: MDPI - Multidisciplinary Digital Publishing Institute 2023
Sujets:
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
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science::PH Physics
Accès en ligne:ONIX_20230105_9783036559056_28
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Résumé: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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