Fractals, metamorphoses and symmetries in quantum field theory

Abstract

The mechanism of spontaneous breakdown of symmetry in quantum field theory is reviewed, the Goldstone theorem derived and the formation of ordered patterns is discussed. Metamorphoses and fractal self-similarity are described in terms of the dynamical rearrangement of symmetry in spontaneously broken symmetry theories. The isomorphism between fractal self-similarity and deformed coherent states is exhibited. It is also discussed how the missing of infrared terms in physical observations is responsible of the metamorphosis processes. The dynamical generation of squeezed, entangled coherent states plays a crucial role in the formation of ordered patterns (morphogenesis). The discussion on metamorphoses and other results extend to condensed matter physics, elementary particles, biological systems and brain studies.