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Article

Renormalization in Quantum Brain Dynamics

by
Akihiro Nishiyama
1,*,
Shigenori Tanaka
1 and
Jack A. Tuszynski
2,3,4
1
Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan
2
Department of Oncology, Cross Cancer Institute, University of Alberta, Edmonton, AB T6G 1Z2, Canada
3
Department of Physics, University of Alberta, Edmonton, AB T6G 2J1, Canada
4
Department of Mechanical and Aerospace Engineering, Corso Duca degli Abruzzi, 24, Politecnico di Torino, 10129 Turin, Italy
*
Author to whom correspondence should be addressed.
AppliedMath 2023, 3(1), 117-146; https://doi.org/10.3390/appliedmath3010009
Submission received: 1 February 2023 / Revised: 14 February 2023 / Accepted: 17 February 2023 / Published: 22 February 2023
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Abstract

We show renormalization in Quantum Brain Dynamics (QBD) in 3+1 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.
Keywords: Quantum Brain Dynamics; Quantum Field Theory; renormalization Quantum Brain Dynamics; Quantum Field Theory; renormalization

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MDPI and ACS Style

Nishiyama, A.; Tanaka, S.; Tuszynski, J.A. Renormalization in Quantum Brain Dynamics. AppliedMath 2023, 3, 117-146. https://doi.org/10.3390/appliedmath3010009

AMA Style

Nishiyama A, Tanaka S, Tuszynski JA. Renormalization in Quantum Brain Dynamics. AppliedMath. 2023; 3(1):117-146. https://doi.org/10.3390/appliedmath3010009

Chicago/Turabian Style

Nishiyama, Akihiro, Shigenori Tanaka, and Jack A. Tuszynski. 2023. "Renormalization in Quantum Brain Dynamics" AppliedMath 3, no. 1: 117-146. https://doi.org/10.3390/appliedmath3010009

APA Style

Nishiyama, A., Tanaka, S., & Tuszynski, J. A. (2023). Renormalization in Quantum Brain Dynamics. AppliedMath, 3(1), 117-146. https://doi.org/10.3390/appliedmath3010009

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