## 2 From the Many-Body Model to the Dissipative Quantum Model  
From observations carried out with EEG, ECoG, fNMR, and other techniques, it appears that myriads of neurons undergo \"in phase\", i.e., coherent, oscillations with amplitude modulations (AM) and phase modulations (PM) [13; 30; 31; 32; 33; 34; 35]. These synchronized patterns form in few ms, have a finite size, persist in a time interval of 80-120 ms, have carrier frequencies in the range of 12-80 Hz (the beta-gamma range), and re-synchronize at frame rates in the theta-alpha range (3-12 Hz). They cover domains of 19 cm in linear size in humans and much of the hemisphere in rabbits and cats [13; 30; 31; 32; 33; 34; 35] (see also [17; 18; 19; 20; 21; 22]). The analysis of the observed time scale and space extension of the AM patterns leads to excluding that they might be generated by propagation of chemicals, which would be too slow. Moreover, cortex patterns are observed [31] to jump abruptly from a receiving state to an active transmitting state. Long-range correlations are not created by the exchange of neurotransmitters, whose propagation is therefore not the cause, rather the effect of the formation of AM patterns; it is by them facilitated. On the other hand, magnetic field and electric current densities sustained by extracellular dendritic trees are too weak to be responsible for the observed rich texture of the AM patterns [13]. Neuronal radio waves (combined electric and magnetic field propagation) are also excluded due to the unbalance between the electric permittivity and magnetic permeability (80:1) of neural tissue. They are excluded also because of the low frequency (<100 Hz) and km wavelengths of em radiation at frequencies of EEG [36]. The very small time scales and the extremely large number of brain states spanned with the observed high efficiency in the brain functional activity led [PERSON] and [PERSON] to suggest that \"new non-classical mechanisms have to be looked for... it is strongly suggestive of a quantum model\" [1], as already mentioned in Section 1. They proposed that the neuronal correlations could be generated by the mechanism of the spontaneous breakdown of symmetry (SBS) in QFT in a similar way as long-range correlations arise in condensed matter physics. General theorems in QFT imply indeed that as a consequence of SBS, long-range correlations are dynamically produced in the system [5; 6; 7; 8; 37]. The system's lowest energy state (the vacuum or ground state) is then a coherent condensate of the quanta, called Nambu-Goldstone (NG) modes, associated with such correlation waves. These NG quanta are massless so that the associated correlation waves may span the whole system volume, taken to be very large (infinite in the QFT limit). For example, the magnetic order in a magnet, measured by the \"order parameter\" magnetization, is generated by the \"spin wave\" correlations, whose associated quanta, coherently condensed in the system vacuum, are called magnons (coherent boson condensation occurs in a wide range of temperatures in many systems, such as ferromagnets, crystals, superfluids, and superconductors; for example, the iron magnetization is lost at 770 \({}^{\circ}\)C; diamond crystal melts at 3545 \({}^{\circ}\)C; kitchen salt (sodium chloride crystal) melts at 804 \({}^{\circ}\)C; the superconductivity of compounds of niobium is lost at \(-153\)\({}^{\circ}\)C, and at \(-252\)\({}^{\circ}\)C for copper and bismuth compounds; coherence phenomena are observed in photosynthesis at ordinary temperatures). We note that the order parameter, which provides a measure of the ordering at the quantum level, behaves, however, as a classical field, in the sense that it is not affected by quantum fluctuations. This is a property due to the coherence of the system ground states, and we see that it allows the transition to the macroscopic classical behavior of the system. We stress that it is not the \"classical limit\" obtained for \(\hbar\to 0\). It is the macroscopic manifestation of the coherent dynamics at the quantum level.