Abstract
We derive time evolution equations, namely the Schrödinger-like equations and the Klein–Gordon equations for coherent fields and the Kadanoff–Baym (KB) equations for quantum fluctuations, in quantum electrodynamics (QED) with electric dipoles in dimensions. Next we introduce a kinetic entropy current based on the KB equations in the first order of the gradient expansion. We show the H-theorem for the leading-order self-energy in the coupling expansion (the Hartree–Fock approximation). We show conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to quantum brain dynamics, that is QED, with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.
Highlights
Numerous attempts to understand memory in a brain have been made over one hundred years starting at the end of 19th century
Our analysis provides the dynamics of both the order parameters with coherent fields and quantum fluctuations for incoherent particles
Total energy consumption to maintain super-radiance in microtubules is consistent with energy consumption in our experiences
Summary
Numerous attempts to understand memory in a brain have been made over one hundred years starting at the end of 19th century. The concrete mechanism of memory still remains an open question in conventional neuroscience [1,2,3]. Conventional neuroscience is based on classical mechanics with neurons connected by synapses. Quantum field theory (QFT) of the brain or quantum brain dynamics (QBD), is one of the hypotheses expected to describe the mechanism of memory in the brain [4,5,6]. Several properties of memory, namely the diversity, the long-term but imperfect stability and nonlocality The QBD can describe these properties by adopting infinitely physically or unitarily inequivalent vacua in QFT, distinguished from quantum mechanics which cannot describe unitarily inequivalence. The vacua or the ground states appearing in SSB describe the stability of the states
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