Relativistic conformal symmetry of neural field propagation in the brain

TL;DR

This paper explores the application of relativistic conformal symmetry to neural field equations, providing exact solutions and revealing that at large distances, neural pulses resemble Yukawa potentials, offering new insights into brain dynamics.

Contribution

It introduces the analysis of neural field propagation under relativistic conformal symmetry and derives exact solutions, linking neural pulses to Yukawa potentials at large scales.

Findings

Exact solutions for neural field equations in 3 and 4 dimensions.

Neural pulses asymptotically resemble Yukawa potentials at large distances.

Relativistic conformal symmetry provides new insights into brain dynamics.

Abstract

In this paper, we address a neural field equation that characterizes spatio-temporal propagation of a neural population pulse. Due that the human brain is a complex system whose constituents interaction give rise to fundamental states of consciousness and behavior, it is crucial to gain insight into its functioning even at relativistic scales. To this end, we study the action of the relativistic conformal group on the accounted neural field propagation equation. In particular, we obtain an exact solution for the field propagation equation when the space-time is 3 or 4 dimensional. Furthermore, in the 4 dimensional case and the large distance limit, it is shown that the neural population pulse becomes a Yukawa potential.