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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| Jazyk: | angličtina |
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MDPI - Multidisciplinary Digital Publishing Institute
2023
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| On-line přístup: | ONIX_20230105_9783036559056_28 |
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| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-95799 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-957992024-03-28T03:32:40Z Selected Topics in Gravity, Field Theory and Quantum Mechanics Duplij, Steven Walker, Michael L. 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 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. 2023-01-05T12:33:22Z 2023-01-05T12:33:22Z 2022 book ONIX_20230105_9783036559056_28 9783036559056 9783036559063 https://directory.doabooks.org/handle/20.500.12854/95799 eng image/jpeg Attribution 4.0 International https://mdpi.com/books/pdfview/book/6455 https://mdpi.com/books/pdfview/book/6455 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-5906-3 10.3390/books978-3-0365-5906-3 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036559056 9783036559063 348 Basel open access |
| spellingShingle | 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 Selected Topics in Gravity, Field Theory and Quantum Mechanics |
| title | Selected Topics in Gravity, Field Theory and Quantum Mechanics |
| title_full | Selected Topics in Gravity, Field Theory and Quantum Mechanics |
| title_fullStr | Selected Topics in Gravity, Field Theory and Quantum Mechanics |
| title_full_unstemmed | Selected Topics in Gravity, Field Theory and Quantum Mechanics |
| title_short | Selected Topics in Gravity, Field Theory and Quantum Mechanics |
| title_sort | selected topics in gravity field theory and quantum mechanics |
| topic | 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 |
| topic_facet | 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 |
| url | ONIX_20230105_9783036559056_28 |