Symmetry: from Galois to Superstrings
DOI link for Symmetry: from Galois to Superstrings
Symmetry: from Galois to Superstrings book
In the 1760s, one of the primary interests of the French mathematician Lagrange concerned the solution of algebraic equations. Galois' achievement, in the context of the solution of polynomial equations, was not only his demonstration of the fact that any such equation could be associated with a 'symmetry group', but that these symmetry groups could be separated into two kinds called 'reducible' and 'irreducible'. Galois showed that the general polynomial equations of fifth or higher order possessed symmetry groups that could not be reduced to the degree necessary to permit an algebraic solution. Most physicists are pinning their hopes on a new theory that hopefully will enable gravity to finally be united with the other three forces of nature in a quantized super-unified theory. More formally they are known as 'superstring' theories. Supersymmetry, which associates fermions and bosons as two 'rotational' states of the same superparticle is a geometrical symmetry.