Goals and Perspectives

Abstract

The hypothesis that the fundamental laws in Nature have the scale and conformal symmetries has been very attractive to many physicists. The idea is interesting by the fact that the conformal symmetry is the highest space-time symmetry. Besides the transformations of the Poincaré group it includes the transformations which preserve angles between world lines

$${x_\mu } \to \lambda {x_\mu },{\kern 1pt} {\kern 1pt} {x_\mu } \to \frac{{{x_\mu } + {a_\mu }{x^2}}}{{1 + 2ax + {a^2}{x^2}}}$$

(1.1)

In fact, this symmetry is a reflection of an old idea that the matter is structureless. Our concepts on the problem of how, and in which specific physical background is this symmetry realized, have however been gradually changing.