International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2365-2371

Connection space approach to ambiguities of gauge theories

R. Aldrovandi and A. L. Barbosa

Instituto de Física Teórica, Universidade Estadual Paulista “Júlio de Mesquita Filho”, Rua Pamplona 145, São Paulo CEP 01405-900, Brazil

Received 24 October 2004; Revised 17 July 2005

Copyright © 2005 R. Aldrovandi and A. L. Barbosa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two distinct gauge potentials can have the same field strength, in which case they are said to be “copies” of each other. The consequences of this ambiguity for the general affine space 𝒜 of gauge potentials are examined. Any two potentials are connected by a straight line in 𝒜, but a straight line going through two copies either contains no other copy or is entirely formed by copies.