Brain and Quantum Field Theory Notes on monumental discussions presenting

Yasushi Takahashi, Mari Jibu

Mari Jibu, Kunio Yasue

Mari Jibu, Kunio Yasue

Sisir Roy, Menas C. Kafatos

The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of brain permits any kind of smooth geometric notion like Hilbert structure or four dimensional Minkowskian structure for quantum field theory. The present understanding of brain function clearly denies any kind of space-time representation in Minkowskian sense. However, three dimensional space and one time can be assigned to the neuromanifold and the concept of probabilistic geometry is shown to be appropriate framework to understand the brain dynamics. The possibility of quantum structure is also discussed in this framework.

Sisir Roy, Menas C. Kafatos

Abstract. The recent controversy of applicability of quantum formalism to brain dynamics has been critically analyzed. PELLIONISZ and LLINÁS (1982) proposed a functional geometry to understand the internal representation of the events associated to the space-timing of moving objects in the external world. The joint representation of space and time associated to an event as understood by the brain is shown to be different from that understood in modern physics. This indicates that the four-dimensional geometry i.e. Minkowski geometry is not an appropriate description for the internal world. If it is to be the case, the applicability of any kind of quantum field theory in modeling brain function has to be analyzed with great care. Here, the issue of applicability of quantum mechanics to brain function has been discussed in general, from an anatomical perspective and then particular emphasis has been given to the applicability of quantum field theory. 1.

Jan Govaerts A

These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract algebraic aspects of quantisation in contrast to more standard treatments of such issues, while also bridging towards the path integral formulation of quantisation. A discussion of the (first) Noether theorem and Lie symmetries is also included to complement the presentation. Emphasis is put throughout, as illustrative examples threading the presentation, on the quantum harmonic oscillator and the dynamics of a charged particle coupled to the electromagnetic field, with the ambition to bring the reader onto the threshold of relativistic quantum field theories with their local gauge invariances as a natural framework for describing relativistic quantum particles in interaction and carrying specific conserved charges.