Renormalization in Quantum Brain Dynamics
We show renormalization in Quantum Brain Dynamics (QBD) in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></semantics>&...
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| Format: | Article |
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MDPI AG
2023-02-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/3/1/9 |
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| author | Akihiro Nishiyama Shigenori Tanaka Jack A. Tuszynski |
| author_facet | Akihiro Nishiyama Shigenori Tanaka Jack A. Tuszynski |
| author_sort | Akihiro Nishiyama |
| collection | DOAJ |
| description | We show renormalization in Quantum Brain Dynamics (QBD) in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> dimensions, namely Quantum Electrodynamics with water rotational dipole fields. First, we introduce the Lagrangian density for QBD involving terms of water rotational dipole fields, photon fields and their interactions. Next, we show Feynman diagrams with 1-loop self-energy and vertex function in dipole coupling expansion in QBD. The counter-terms are derived from the coupling expansion of the water dipole moment. Our approach will be applied to numerical simulations of Kadanoff–Baym equations for water dipoles and photons to describe the breakdown of the rotational symmetry of dipoles, namely memory formation processes. It will also be extended to the renormalization group method for QBD with running parameters in multi-scales. |
| first_indexed | 2024-03-11T06:59:53Z |
| format | Article |
| id | doaj.art-bd22fea9d69e418c85c33fa0b4e42027 |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-11T06:59:53Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-bd22fea9d69e418c85c33fa0b4e420272023-11-17T09:20:05ZengMDPI AGAppliedMath2673-99092023-02-013111714610.3390/appliedmath3010009Renormalization in Quantum Brain DynamicsAkihiro Nishiyama0Shigenori Tanaka1Jack A. Tuszynski2Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, JapanGraduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, JapanDepartment of Oncology, Cross Cancer Institute, University of Alberta, Edmonton, AB T6G 1Z2, CanadaWe show renormalization in Quantum Brain Dynamics (QBD) in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> dimensions, namely Quantum Electrodynamics with water rotational dipole fields. First, we introduce the Lagrangian density for QBD involving terms of water rotational dipole fields, photon fields and their interactions. Next, we show Feynman diagrams with 1-loop self-energy and vertex function in dipole coupling expansion in QBD. The counter-terms are derived from the coupling expansion of the water dipole moment. Our approach will be applied to numerical simulations of Kadanoff–Baym equations for water dipoles and photons to describe the breakdown of the rotational symmetry of dipoles, namely memory formation processes. It will also be extended to the renormalization group method for QBD with running parameters in multi-scales.https://www.mdpi.com/2673-9909/3/1/9Quantum Brain DynamicsQuantum Field Theoryrenormalization |
| spellingShingle | Akihiro Nishiyama Shigenori Tanaka Jack A. Tuszynski Renormalization in Quantum Brain Dynamics AppliedMath Quantum Brain Dynamics Quantum Field Theory renormalization |
| title | Renormalization in Quantum Brain Dynamics |
| title_full | Renormalization in Quantum Brain Dynamics |
| title_fullStr | Renormalization in Quantum Brain Dynamics |
| title_full_unstemmed | Renormalization in Quantum Brain Dynamics |
| title_short | Renormalization in Quantum Brain Dynamics |
| title_sort | renormalization in quantum brain dynamics |
| topic | Quantum Brain Dynamics Quantum Field Theory renormalization |
| url | https://www.mdpi.com/2673-9909/3/1/9 |
| work_keys_str_mv | AT akihironishiyama renormalizationinquantumbraindynamics AT shigenoritanaka renormalizationinquantumbraindynamics AT jackatuszynski renormalizationinquantumbraindynamics |